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Maxwell–Boltzmann statistics

In statistical mechanics, Maxwell–Boltzmann statistics describes the distribution of classical material particles over various energy states in thermal equilibrium. It is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.

The expected number of particles with energy $$\varepsilon_i$$ for Maxwell–Boltzmann statistics is

 * $$\langle N_i \rangle = \frac {g_i} {e^{(\varepsilon_i - \mu)/kT}} = \frac{N}{Z}\,g_i e^{-\varepsilon_i/kT},$$

where:
 * $$\varepsilon_i$$ is the energy of the i-th energy level,
 * $$\langle N_i \rangle$$ is the average number of particles in the set of states with energy $$\varepsilon_i$$,
 * $$g_i$$ is the degeneracy of energy level i, that is, the number of states with energy $$\varepsilon_i$$ which may nevertheless be distinguished from each other by some other means,
 * μ is the chemical potential,
 * k is the Boltzmann constant,
 * T is absolute temperature,
 * N is the total number of particles: $$N = \sum_i N_i,$$
 * Z is the partition function: $$Z = \sum_i g_i e^{-\varepsilon_i/kT},$$
 * e is Euler's number

Equivalently, the number of particles is sometimes expressed as

 * $$\langle N_i \rangle = \frac {1} {e^{(\varepsilon_i - \mu)/kT}} = \frac{N}{Z}\,e^{-\varepsilon_i/kT},$$

where the index i now specifies a particular state rather than the set of all states with energy $$\varepsilon_i$$, and $Z = \sum_i e^{-\varepsilon_i/kT}$.

History
Maxwell–Boltzmann statistics grew out of the Maxwell–Boltzmann distribution, most likely as a distillation of the underlying technique. The distribution was first derived by Maxwell in 1860 on heuristic grounds. Boltzmann later, in the 1870s, carried out significant investigations into the physical origins of this distribution. The distribution can be derived on the ground that it maximizes the entropy of the system.

Applicability

Maxwell–Boltzmann statistics is used to derive the Maxwell–Boltzmann distribution of an ideal gas. However, it can also be used to extend that distribution to particles with a different energy–momentum relation, such as relativistic particles (resulting in Maxwell–Jüttner distribution), and to other than three-dimensional spaces.

Maxwell–Boltzmann statistics is often described as the statistics of "distinguishable" classical particles. In other words, the configuration of particle A in state 1 and particle B in state 2 is different from the case in which particle B is in state 1 and particle A is in state 2. This assumption leads to the proper (Boltzmann) statistics of particles in the energy states, but yields non-physical results for the entropy, as embodied in the Gibbs paradox.

At the same time, there are no real particles that have the characteristics required by Maxwell–Boltzmann statistics. Indeed, the Gibbs paradox is resolved if we treat all particles of a certain type (e.g., electrons, protons,photon etc.) as principally indistinguishable. Once this assumption is made, the particle statistics change. The change in entropy in the entropy of mixing example may be viewed as an example of a non-extensive entropy resulting from the distinguishability of the two types of particles being mixed.

Quantum particles are either bosons (following instead Bose–Einstein statistics) or fermions (subject to the Pauli exclusion principle, following instead Fermi–Dirac statistics). Both of these quantum statistics approach the Maxwell–Boltzmann statistics in the limit of high temperature and low particle density.

Derivations
Maxwell–Boltzmann statistics can be derived in various statistical mechanical thermodynamic ensembles: In each case it is necessary to assume that the particles are non-interacting, and that multiple particles can occupy the same state and do so independently.
 * The grand canonical ensemble, exactly.
 * The canonical ensemble, exactly.
 * The microcanonical ensemble, but only in the thermodynamic limit.

Derivation from microcanonical ensemble
Suppose we have a container with a huge number of very small particles all with identical physical characteristics (such as mass, charge, etc.). Let's refer to this as the system. Assume that though the particles have identical properties, they are distinguishable. For example, we might identify each particle by continually observing their trajectories, or by placing a marking on each one, e.g., drawing a different number on each one as is done with lottery balls.

The particles are moving inside that container in all directions with great speed. Because the particles are speeding around, they possess some energy. The Maxwell–Boltzmann distribution is a mathematical function that describes about how many particles in the container have a certain energy. More precisely, the Maxwell–Boltzmann distribution gives the non-normalized probability (this means that the probabilities do not add up to 1) that the state corresponding to a particular energy is occupied.

In general, there may be many particles with the same amount of energy $$\varepsilon$$. Let the number of particles with the same energy $$\varepsilon_1$$ be $$N_1$$, the number of particles possessing another energy $$\varepsilon_2$$ be $$N_2$$, and so forth for all the possible energies $$\{ \varepsilon_i \mid i = 1, 2, 3, \ldots\}.$$ To describe this situation, we say that $$N_i$$ is the occupation number of the energy level $$i.$$ If we know all the occupation numbers $$\{N_i \mid i=1,2,3,\ldots\},$$ then we know the total energy of the system. However, because we can distinguish between which particles are occupying each energy level, the set of occupation numbers $$ \{ N_i \mid i=1,2,3,\ldots\}$$ does not completely describe the state of the system. To completely describe the state of the system, or the microstate, we must specify exactly which particles are in each energy level. Thus when we count the number of possible states of the system, we must count each and every microstate, and not just the possible sets of occupation numbers.

To begin with, assume that there is only one state at each energy level $$i$$ (there is no degeneracy). What follows next is a bit of combinatorial thinking which has little to do in accurately describing the reservoir of particles. For instance, let's say there is a total of $$k$$ boxes labelled $$a,b,\ldots,k$$. With the concept of combination, we could calculate how many ways there are to arrange $$N$$ into the set of boxes, where the order of balls within each box isn’t tracked. First, we select $$N_a$$ balls from a total of $$N$$ balls to place into box $$a$$, and continue to select for each box from the remaining balls, ensuring that every ball is placed in one of the boxes. The total number of ways that the balls can be arranged is

\begin{align} W & = \frac{N!}{N_a!\cancel{(N-N_a)!}} \times \frac{\cancel{(N-N_a)!}}{N_b!\cancel{(N-N_a-N_b)!}} \times \frac{\cancel{(N-N_a-N_b)!}}{N_c!\cancel{(N-N_a-N_b-N_c)!}} \times \cdots \times \frac{\cancel{(N-\cdots-N_\ell)!}}{N_k!(N-\cdots-N_\ell-N_k)!} \\[8pt] & = \frac{N!}{N_a!N_b!N_c!\cdots N_k!(N-N_a-\cdots-N_\ell-N_k)!} \end{align} $$

As every ball has been placed into a box, $$(N - N_a - N_b - \cdots - N_k)! = 0! = 1$$, and we simplify the expression as

W = N!\prod_{\ell=a,b,\ldots}^k \frac{1}{N_\ell!} $$

This is just the multinomial coefficient, the number of ways of arranging N items into k boxes, the l-th box holding Nl items, ignoring the permutation of items in each box.

Now, consider the case where there is more than one way to put $$ N_i $$ particles in the box $$ i $$ (i.e. taking the degeneracy problem into consideration). If the $$ i $$-th box has a "degeneracy" of $$g_i$$, that is, it has $$g_i$$ "sub-boxes" ($$ g_i $$ boxes with the same energy $$ \varepsilon_i $$. These states/boxes with the same energy are called degenerate states.), such that any way of filling the $$ i $$-th box where the number in the sub-boxes is changed is a distinct way of filling the box, then the number of ways of filling the i-th box must be increased by the number of ways of distributing the $$N_i$$ objects in the $$g_i$$ "sub-boxes". The number of ways of placing $$N_i$$ distinguishable objects in $$g_i$$ "sub-boxes" is $$g_i^{N_i}$$ (the first object can go into any of the $$g_i$$ boxes, the second object can also go into any of the $$g_i$$ boxes, and so on). Thus the number of ways $$W$$ that a total of $$N$$ particles can be classified into energy levels according to their energies, while each level $$i$$ having $$g_i$$ distinct states such that the i-th level accommodates $$N_i$$ particles is:

 * $$W=N!\prod_{i}\frac{g_i^{N_i}}{N_i!}$$

This is the form for W first derived by Boltzmann. Boltzmann's fundamental equation $$S=k\,\ln W$$ relates the thermodynamic entropy S to the number of microstates W, where k is the Boltzmann constant. It was pointed out by Gibbs however, that the above expression for W does not yield an extensive entropy, and is therefore faulty. This problem is known as the Gibbs paradox. The problem is that the particles considered by the above equation are not indistinguishable. In other words, for two particles (A and B) in two energy sublevels the population represented by [A,B] is considered distinct from the population [B,A] while for indistinguishable particles, they are not. If we carry out the argument for indistinguishable particles, we are led to the Bose–Einstein expression for W:

 * $$W=\prod_i \frac{(N_i+g_i-1)!}{N_i!(g_i-1)!}$$

The Maxwell–Boltzmann distribution follows from this Bose–Einstein distribution for temperatures well above absolute zero, implying that $$g_i\gg 1$$. The Maxwell–Boltzmann distribution also requires low density, implying that $$g_i\gg N_i$$. Under these conditions, we may use Stirling's approximation for the factorial:

 * $$N! \approx N^N e^{-N},$$

to write:

 * $$W\approx\prod_i \frac{(N_i+g_i)^{N_i+g_i}}{N_i^{N_i}g_i^{g_i}}\approx\prod_i \frac{g_i^{N_i}(1+N_i/g_i)^{g_i}}{N_i^{N_i}}$$

Using the fact that $$(1+N_i/g_i)^{g_i}\approx e^{N_i}$$ for $$g_i\gg N_i$$ we can again use Stirling's approximation to write:

 * $$W\approx\prod_i \frac{g_i^{N_i}}{N_i!}$$

This is essentially a division by N! of Boltzmann's original expression for W, and this correction is referred to as .

We wish to find the $$N_i$$ for which the function $$W$$ is maximized, while considering the constraint that there is a fixed number of particles $\left(N=\sum N_i\right)$ and a fixed energy $\left(E=\sum N_i \varepsilon_i\right)$  in the container. The maxima of $$W$$ and $$\ln(W)$$ are achieved by the same values of $$N_i$$ and, since it is easier to accomplish mathematically, we will maximize the latter function instead. We constrain our solution using Lagrange multipliers forming the function:

 * $$f(N_1,N_2,\ldots,N_n) = \textstyle \ln(W)+\alpha(N-\sum N_i) + \beta(E-\sum N_i \varepsilon_i)$$
 * $$\ln W=\ln\left[\prod_{i=1}^{n}\frac{g_i^{N_i}}{N_i!}\right] \approx \sum_{i=1}^n\left(N_i\ln g_i-N_i\ln N_i + N_i\right)$$

Finally

 * $$f(N_1,N_2,\ldots,N_n)=\alpha N +\beta E + \sum_{i=1}^n\left(N_i\ln g_i-N_i\ln N_i + N_i-(\alpha+\beta\varepsilon_i) N_i\right)$$

In order to maximize the expression above we apply Fermat's theorem (stationary points), according to which local extrema, if exist, must be at critical points (partial derivatives vanish):

 * $$\frac{\partial f}{\partial N_i}=\ln g_i-\ln N_i -(\alpha+\beta\varepsilon_i) = 0$$

By solving the equations above ($$i=1\ldots n$$) we arrive to an expression for $$N_i$$:

 * $$N_i = \frac{g_i}{e^{\alpha+\beta \varepsilon_i}} $$

Substituting this expression for $$N_i$$ into the equation for $$\ln W$$ and assuming that $$N \gg 1$$ yields:

 * $$\ln W = (\alpha+1) N+\beta E\,$$

or, rearranging:

 * $$E=\frac{\ln W}{\beta}-\frac{N}{\beta}-\frac{\alpha N}{\beta}$$

Boltzmann realized that this is just an expression of the Euler-integrated fundamental equation of thermodynamics. Identifying E as the internal energy, the Euler-integrated fundamental equation states that :

 * $$E=TS-PV+\mu N$$

where T is the temperature, P is pressure, V is volume, and μ is the chemical potential. Boltzmann's equation $$S=k \ln W$$ is the realization that the entropy is proportional to $$\ln W$$ with the constant of proportionality being the Boltzmann constant. Using the ideal gas equation of state (PV = NkT), It follows immediately that $$\beta=1/kT$$ and $$\alpha=-\mu/kT$$ so that the populations may now be written:

 * $$N_i = \frac{g_i}{e^{(\varepsilon_i-\mu)/(kT)}} $$

Note that the above formula is sometimes written:

 * $$N_i = \frac{g_i}{e^{\varepsilon_i/kT}/z} $$

where $$z=\exp(\mu/kT)$$ is the absolute activity.

Alternatively, we may use the fact that

 * $$\sum_i N_i=N$$

to obtain the population numbers as

 * $$N_i = N\frac{g_i e^{-\varepsilon_i/kT}}{Z} $$

where Z is the partition function defined by:

 * $$Z = \sum_i g_i e^{-\varepsilon_i/kT}$$

In an approximation where εi is considered to be a continuous variable, the Thomas–Fermi approximation yields a continuous degeneracy g proportional to $$\sqrt{\varepsilon}$$ so that:

\frac{\sqrt{\varepsilon}\,e^{-\varepsilon/k T}}{\int_0^\infty\sqrt{\varepsilon}\,e^{-\varepsilon/k T}} = \frac{\sqrt{\varepsilon}\,e^{-\varepsilon/k T}}{\frac{\sqrt{\pi}}{2}(kT)^{3/2}} = \frac{2\sqrt{\varepsilon}\,e^{-\varepsilon/k T}}{\sqrt{\pi(kT)^3}} $$

which is just the Maxwell–Boltzmann distribution for the energy.

Derivation from canonical ensemble
In the above discussion, the Boltzmann distribution function was obtained via directly analysing the multiplicities of a system. Alternatively, one can make use of the canonical ensemble. In a canonical ensemble, a system is in thermal contact with a reservoir. While energy is free to flow between the system and the reservoir, the reservoir is thought to have infinitely large heat capacity as to maintain constant temperature, T, for the combined system.

In the present context, our system is assumed to have the energy levels $$\varepsilon _i$$ with degeneracies $$g_i$$. As before, we would like to calculate the probability that our system has energy $$\varepsilon_i$$.

If our system is in state $$\; s_1$$, then there would be a corresponding number of microstates available to the reservoir. Call this number $$\; \Omega _ R (s_1)$$. By assumption, the combined system (of the system we are interested in and the reservoir) is isolated, so all microstates are equally probable. Therefore, for instance, if $$ \; \Omega _ R (s_1) = 2 \; \Omega _ R (s_2) $$, we can conclude that our system is twice as likely to be in state $$\; s_1$$ than $$\; s_2$$. In general, if $$\; P(s_i)$$ is the probability that our system is in state $$\; s_i$$,

 * $$\frac{P(s_1)}{P(s_2)} = \frac{\Omega _ R (s_1)}{\Omega _ R (s_2)}.$$

Since the entropy of the reservoir $$\; S_R = k \ln \Omega _R$$, the above becomes

 * $$\frac{P(s_1)}{P(s_2)} = \frac{ e^{S_R(s_1)/k} }{ e^{S_R(s_2)/k} } = e^{(S_R (s_1) - S_R (s_2))/k}.$$

Next we recall the thermodynamic identity (from the first law of thermodynamics):

 * $$d S_R = \frac{1}{T} (d U_R + P \, d V_R - \mu \, d N_R).$$

In a canonical ensemble, there is no exchange of particles, so the $$d N_R$$ term is zero. Similarly, $$d V_R = 0.$$ This gives

 * $$ S_R (s_1) - S_R (s_2) = \frac{1}{T} (U_R (s_1) - U_R (s_2)) = - \frac{1}{T} (E(s_1) - E(s_2)),$$

where $$ U_R (s_i) $$ and $$ E(s_i) $$ denote the energies of the reservoir and the system at $$s_i$$, respectively. For the second equality we have used the conservation of energy. Substituting into the first equation relating $$P(s_1), \; P(s_2)$$:

\frac{P(s_1)}{P(s_2)} = \frac{ e^{ - E(s_1) / kT } }{ e^{ - E(s_2) / kT} }, $$

which implies, for any state s of the system

P(s) = \frac{1}{Z} e^{- E(s) / kT}, $$

where Z is an appropriately chosen "constant" to make total probability 1. (Z is constant provided that the temperature T is invariant.)

 * $$ Z = \sum _s e^{- E(s) / kT}, $$

where the index s runs through all microstates of the system. Z is sometimes called the Boltzmann sum over states (or "Zustandssumme" in the original German). If we index the summation via the energy eigenvalues instead of all possible states, degeneracy must be taken into account. The probability of our system having energy $$\varepsilon _i$$ is simply the sum of the probabilities of all corresponding microstates:

 * $$P (\varepsilon _i) = \frac{1}{Z} g_i e^{- \varepsilon_i / kT}$$

where, with obvious modification,

 * $$Z = \sum _j g_j e^{- \varepsilon _j / kT},$$

this is the same result as before.

Comments on this derivation:
 * Notice that in this formulation, the initial assumption "... suppose the system has total N particles..." is dispensed with. Indeed, the number of particles possessed by the system plays no role in arriving at the distribution. Rather, how many particles would occupy states with energy $$\varepsilon _i$$ follows as an easy consequence.
 * What has been presented above is essentially a derivation of the canonical partition function. As one can see by comparing the definitions, the Boltzmann sum over states is equal to the canonical partition function.
 * Exactly the same approach can be used to derive Fermi–Dirac and Bose–Einstein statistics. However, there one would replace the canonical ensemble with the grand canonical ensemble, since there is exchange of particles between the system and the reservoir. Also, the system one considers in those cases is a single particle state, not a particle. (In the above discussion, we could have assumed our system to be a single atom.)

title: Maxwell–Boltzmann statistics


text:
Talk:Cold war (term)

Older comments
If you must combine these articles, they need to be under Cold War, not Cold war, as The Cold War was a specific war and hence a proper noun. --nknight 13:00 Jan 17, 2003 (UTC)

I don't think the Taiwan issue qualifies as a cold war. It's more of an unresolved civil war. --Jiang 20:44 21 Jul 2003 (UTC)

All linking articles about the Cold War have now been redirected to Cold War. --GCarty 17:30 2 Nov 2003 (UTC)

Regarding moving this to Wiktionary, essentially it's the equivalent of what many folks have wanted to do -- merge this with Cold War (proper) and explain the concept of a Cold war within that article. Jiang is correct re: China vs. Taiwan, is not referred to as a cold war. It's a continuation of civil war that goes back to the early part of the 20th century. Greece and Turkey were seen as critical countries during the Cold War because the USSR would see it as a NATO weakness if there was a conflict, but as such, they are not referred to widely as being involved in a cold war. That said, there is no real reason for this article to exist alone. It should be merged with the Cold War article. Fuzheado 07:39, 9 Mar 2004 (UTC)

Cold war and Cold War
I searched for "cold war" ended up here was loking for "Cold War" article... whats going on here? --kunjan1029 05:26, Apr 19, 2005 (UTC)

Cold War- Cuban Missile Crisis
We Need More Information on this Topic! It was an important part of Cold War History! Čóļđ Ŵãř is an Important Even wich needs all the information!

 * The Cuban Missle Crisis was part of the Cold War, and is not usually in itself considered a cold war. Wikiacc (?) 17:00, 26 February 2006 (UTC)

eso es pura mentira bola de creidos no sirven para nada —Preceding unsigned comment added by 206.78.191.178 (talk) 18:33, 13 May 2011 (UTC)

India - Pakistan
Is the situation between India and Pakistan not considered a cold war? —Preceding unsigned comment added by THE DJA (talk • contribs) 11:57, 5 April 2008 (UTC) its all a bunch of bull —Preceding unsigned comment added by 65.19.74.215 (talk) 14:58, 22 March 2010 (UTC)

What?
Isn't it supposed to be United States and Israel vs. Iran, or am I missing something here? Sirius85 (talk) 18:50, 14 July 2009 (UTC)

Chicken or Egg
Which came first: the war tactic or the conflict? Did the term inspire the name of the conflict or did the conflict inspire the term? 76.179.52.183 (talk) 18:24, 9 March 2010 (UTC)

Russian Empire
From the article: "1871–1914: United Kingdom, France, and Russian Empire vs. Germany and Austria–Hungary set off by the formation of the German Empire, which politically and geographically challenged the older empires of Europe." I disagree with the Russian Empire standing on the side of France and the UK. The 'Dreikaiserbund' in 1873 established quite a strong relationship between Germany, Austria and Russia. It was only in the last years before WW1 that Russia moved over to the France-UK side, starting with the Franco-Russian alliance in 1893. —Preceding unsigned comment added by 195.240.84.155 (talk) 14:01, 5 December 2010 (UTC)
 * A good point, and I have altered the text (and the start date) accordingly. Beyond My Ken (talk) 17:31, 5 December 2010 (UTC)

"New" Theories on the Etymology
Anders Stephanson from Columbioa University quite efficiently and comprehensively disproves the notion of Don Juan being the primal source of the term. See this link to his essay., I shall also post it to the 'See Also'. 195.35.252.14 (talk) 16:13, 31 October 2013 (UTC)

Proposed merge with Cold War II

 * The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

The "Cold War II" page was created as a response to the possible tensions between the Russian and the West. Later, the section about the China–US relations was added. Sections about other relations were already moved to the article, "Cold war (general term)." Shall we do the same to this article? George Ho (talk) 07:16, 20 November 2016 (UTC)

Survey

 * Oppose A separate Cold War II makes logical sense, because it is a "legitimate" successor, a "resurgence" of Cold War. The rest of "cold wars" are not. Staszek Lem (talk) 17:16, 20 November 2016 (UTC)
 * MergeThe Cold War II article, is short, and can be merged into this article, as a cold war topic. If the Cold War II topic grows it can be split into its own article.CuriousMind01 (talk) 13:22, 21 November 2016 (UTC)
 * Merge: As per CuriousMind01, article splitting is always an option. Otr500 (talk) 21:56, 27 November 2016 (UTC)
 * Merge: Mostly because I don't think that Cold War II is the wrong title for an article about current US/Russia relations. The cold war that followed WWII was marked by massive military spending, spying, deep suspicion and relentless propaganda about communism vs. capitalism.  While some of these things might exist in the current climate, they are simply too different. Elmmapleoakpine (talk) 23:18, 28 November 2016 (UTC)
 * Oppose. Cold War II seems to refer to just Russia/China vs. Western tensions. Cold War (general term) refers to the use of the phrase cold war in general, and more minor diplomatic standoffs labelled cold wars by RS. Both articles are a decent length, and I see no reason to merge. Patar knight - chat/contributions 04:32, 3 December 2016 (UTC)
 * Oppose. Cold War II presupposes the postwar Cold War ever ended. I think that's a contentious view without consensus in the academic and foreign relations communities.  The merger should be in reverse order, merging Cold War II with Cold War to remove the inference that a separate or new phenomenon is occurring rather than this being a continuation of post war hostility.  Invited to comment here by Legobot.   Peter S Strempel  |  Talk  04:02, 4 December 2016 (UTC)
 * Oppose – While not the longest article out there, there is enough material for a standalone article, and the topic is a "successor" to the Cold War between the Soviet Union and the United States and their respective allies. Dustin  ( talk ) 07:34, 9 December 2016 (UTC)
 * Oppose. Well researched and good references documenting the topic. Sagecandor (talk) 07:27, 10 December 2016 (UTC)
 * Oppose - It is an entirely separate phenomenon that is described by reference to Cold War for lack of a better universally acknowledged term, thus far. As to its length, it has recently been drastically cut, which remains a dubious move.Axxxion (talk) 16:49, 12 December 2016 (UTC)
 * Merge: As per CuriousMind01 and Otr500. Borsoka (talk) 04:31, 13 December 2016 (UTC)
 * Oppose: Cold War II is about specific conflicts/scenarios, not the general term. Legoless (talk) 11:56, 13 December 2016 (UTC)

Discussion
Peter, I want to confront you about inserting "original research" into Cold War-related discussions. While WP:NOR does not apply to talk pages, your proposal (merging into "Cold War") might violate the policy. If you are certain that Cold War has not ended, please either add stuff at Historiography of the Cold War or discuss the run of the Cold War at Talk:Historiography of the Cold War. You can repeatedly say the same arguments over and over as you did here and at Talk:Cold War II. I fear that your rationale and proposal would be discarded as one of unverified "conspiracy theories". But I must cooperate with you, and you must do the same with me. I found just this source, that source, this source, that source. George Ho (talk) 05:07, 4 December 2016 (UTC); edited, 05:09, 4 December 2016 (UTC)
 * Your grammar makes it difficult to unpick what you are saying. nevertheless, let me just point out that I was invited to comment by Legobot as an impartial observer.  That I should express the same opinion about relate dtopics strikes me as indicating i have the same opinion on the same topic, not an attempt to do anything 'over and over'.  To translate that into colloquial language: I don't much care what rules you think you know, what the decision will be, or what your own agenda is.  I gave my opinion as an educated polymath whose reading list and understandings exceed any curated factoid link list. Wikipedia editors on this page will now choose to do exactly as they like, which is how things work around here, and reality be damned.  Peter S Strempel  |  Talk  10:34, 9 December 2016 (UTC)
 * Apologies for my... what would be the word you call it when I write less sensible words? Anyway, I'll rephrase for you, but I'm including the link that I discovered today. The last time you edited an article was 2013, Peter, three years ago. Why making an opinion rather than add content or fix typos and grammar in articles? Or why not become an analyst or a conspiracy theorist on Cold War instead of making a complaint or something? Or why not go to the website of Wikipediocracy and post something bad about Wikipedia? Or why not publish a book about the Cold War? George Ho (talk) 11:17, 9 December 2016 (UTC)

Dustin, the consensus agreed that "Cold War II" is not a successor to the "Cold War". --George Ho (talk) 08:17, 9 December 2016 (UTC)
 * It seems that the consensus you mentioned had much to do with the implications of the title, which I am not arguing. Additionally, there was only limited participation in that discussion, even though I may agree with certain elements of its outcome. In this "cold war" (which has been mentioned in a number of sources, real or not), the two factions still remain mostly the same, with the more dominant usage involving Russia (in place of the Soviet Union) on one side and the United States and allies on the other. Even if you put the "successor" bit aside, I still do not see a compelling reason to merge Cold War II into this article (which it is larger than anyway). Dustin  ( talk ) 01:01, 10 December 2016 (UTC)
 * I added a section about China vs US months ago, Dustin. George Ho (talk) 05:48, 10 December 2016 (UTC)
 * I am well aware of that. I said "dominant," and Russia vs. United States is definitely more common than China vs. United States. Dustin  ( talk ) 06:29, 10 December 2016 (UTC)
 * And the title was discussed again, Dustin; the consensus said to retain that title. --George Ho (talk) 07:39, 10 December 2016 (UTC)
 * I don't see why that is supposed to be relevant. Dustin  ( talk ) 19:53, 10 December 2016 (UTC)
 * Oh, no. It's just for the reminder; that's all. George Ho (talk) 21:39, 10 December 2016 (UTC)

Axxxion, we have used Talk:Cold War II to reduce article issues, like original research and advocacy and propaganda. With a lot of talking, the article content was trimmed down from this to that to that to what it is now. I haven't seen you comment about the China vs. US yet. You were solely concerned about the Russia–Western relations, weren't you? George Ho (talk) 11:03, 13 December 2016 (UTC)
 * I wonder what you are after: want to pick my brains on China. Know very little of the subject, but it is obvious the Chinese themselves are not about to be sold on this Western notion of "Cold War". They will just do real war when the chips are down. But looking at the relevant section in the article, what irks me is total absence of any indication of time there: "increased" when? "deployed" when?, etc.Axxxion (talk) 16:54, 13 December 2016 (UTC)

 * The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

template talk:Cold War
I invite you to the discussion. --George Ho (talk) 03:29, 27 December 2016 (UTC)

Likely origin of term Cold War
I have a document which was written by the Chief of Signal Intelligence for the Germans during World War 2. General Albert Praun. Praun was the Chief Signal Officer of Army High Command and of Supreme Command of Armed Forces (Chef des Heeresnachrichtenwesens). Essentially the top guy for Signal Intelligence for the Germans during WW 2. The document was written by him in March 1950, as Homework for TICOM and the document was so important that it was classified by the NSA up until 28th January 2014, when it was released. The document is written as a history of the radio intelligence and intercept service, and in the introduction, he explicitly details the phrase: cold war of the air waves. It is possibly the origin of the term. It was very important document, which carried weight, from an important man, with the American military industrial complex. Could be. I have a feeling it is, as it was in there..scope_creep (talk) 15:12, 6 August 2017 (UTC)

Cold civil wars
Many commentators have described the state of the U.S. and elsewhere as a "cold civil war", suggesting that the term "cold war" can also refer to conflicts between opposing factions within a country rather than just one between nations as is given in the opening sentence. — Preceding unsigned comment added by Pinus jeffreyi (talk • contribs) 00:20, 14 October 2019 (UTC)

Requested move 10 January 2022

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: moved as proposed since the original request to remove "general" from the title has gone uncontested. There is no consensus on the secondary question of whether to remove the disambiguation altogether. (closed by non-admin page mover) Extraordinary Writ (talk) 05:03, 17 January 2022 (UTC)

Cold war (general term) → Cold war (term) – There's no need to say "general" here. This is the only article on enwiki that uses the disambiguator "general term", while 29 use just "term". I don't see why this should be any different. (N.B.: This is a somewhat unusual case where WP:DIFFCAPS has not been invoked [ → Cold War], but I agree with that status quo. DIFFCAPS is ill-suited for cases where the only difference is the first letter of the second word in a two-word phrase, where many readers won't make a distinction between capitalizing or not capitalizing that letter.) --  Tamzin  [ cetacean needed ] (she/they) 00:56, 10 January 2022 (UTC)
 * Support per nom. -- dyl  x  14:19, 10 January 2022 (UTC)
 * Support alternate move to Cold war Per WP:DIFFCAPS. It can still be clearly separated from the "Cold War" (proper noun) using hatnotes.ZXCVBNM (TALK) 14:47, 10 January 2022 (UTC)
 * Move to Cold war per above comment. Rreagan007 (talk) 05:28, 11 January 2022 (UTC)
 * Support move to Cold war. Showiecz (talk) 10:26, 11 January 2022 (UTC)
 * Move to Cold war - I find anytime an article is disambiguated as (term) or (concept) or the like, its probably a misplaced primary topic. -- Netoholic @ 10:31, 11 January 2022 (UTC)
 * Support move as proposed, oppose move to Cold war, per nom. The vast majority of the incoming links to Cold war refer to the Cold War and I can only imagine that the majority of readers who simply type "cold war" are looking for the 20th century conflict, too; pageviews in any case seem to suggest not many people are looking for the article about the term. Lennart97 (talk) 14:04, 15 January 2022 (UTC)
 * Support move as proposed, oppose move to Cold war, per nom and Lennart97. Additionally, the edit history at Cold war shows that most involved editors there thought that people typing "World war" in the edit box were looking for the US-USSR conflict. Sjö (talk) 16:42, 15 January 2022 (UTC)
 * Support original proposal - per above. Also, eliminating the dab would not be beneficial to the project and its readers. George Ho (talk) 04:24, 17 January 2022 (UTC)

Requested move 31 August 2023

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: not moved. (closed by non-admin page mover) – Material  Works  17:07, 14 September 2023 (UTC)

Cold war (term) → Cold war – Per WP:DIFFCAPS, WP:NCCPT and WP:CONCISE, like the Islamic State and the Islamic state. Parham wiki (talk) 09:32, 31 August 2023 (UTC) — Relisting. ModernDayTrilobite (talk • contribs) 13:45, 7 September 2023 (UTC)
 * Oppose. Cold war has redirected to Cold War, not this page, quite consistently for the past 17 years, indicating that the general term is not the primary topic for the lowercase spelling. Dekimasu よ! 15:53, 31 August 2023 (UTC)
 * Support WP:DIFFCAPS would appear to apply here. Britannica backs this up by calling it the Cold War, with news articles inset within using "cold war" to refer to any form of "cold" conflict. ᴢxᴄᴠʙɴᴍ (ᴛ) 18:31, 31 August 2023 (UTC)
 * Strong oppose - DIFFCAPS allows for ignoring itself when one is way more notable than the other Red   Slash  22:05, 6 September 2023 (UTC)
 * Oppose. It's ordinary for people to search using lowercase letters for things that actually contain uppercase letters. This is asymmetric with the reverse situation: people searching with capital letters are not so likely to be looking for the lowercase topic, and that's the kind of prediction about search intent which forms the basis of DIFFCAPS. So I wouldn't discount Cold War too much; it's still the primary topic. I also agree with Lennart97 from the 2022 RM. Adumbrativus (talk) 08:25, 7 September 2023 (UTC)
 * Note: WikiProject International relations has been notified of this discussion. ModernDayTrilobite (talk • contribs) 13:45, 7 September 2023 (UTC)
 * Note: WikiProject Military history has been notified of this discussion. ModernDayTrilobite (talk • contribs) 13:45, 7 September 2023 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Oppose I think that is the primary topic for the exact title  so WP:PRIMARYREDIRECT may also apply. Skynxnex (talk) 16:05, 7 September 2023 (UTC)
 * Oppose per . Ed [talk] [majestic titan] 17:22, 7 September 2023 (UTC)
 * Oppose, being in agreement with almost everything the opposers above have said. Gog the Mild (talk) 19:43, 7 September 2023 (UTC)
 * Support per WP:DIFFCAPS. Rreagan007 (talk) 04:11, 8 September 2023 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Cold war (term)


text:
Interface (object-oriented programming)

In object-oriented programming, an interface or protocol type is a data type that acts as an abstraction of a class. It describes a set of method signatures, the implementations of which may be provided by multiple classes that are otherwise not necessarily related to each other. A class which provides the methods listed in a protocol is said to adopt the protocol, or to implement the interface.

If objects are fully encapsulated then the protocol is the only way in which they may be accessed by other objects. For example, in Java, the  interface specifies a method   which implementing classes must implement. This means that a sorting method, for example, can sort a collection of any objects of types which implement the Comparable interface, without having to know anything about the inner nature of the class (except that two of these objects can be compared by means of ).

Some programming languages provide explicit language support for protocols (Ada, C#, D, Dart, Delphi, Go, Java, Logtalk, Object Pascal, Objective-C, OCaml, PHP, Racket, Seed7, Swift, Python 3.8). In languages supporting multiple inheritance, such as C++, interfaces are implemented as abstract classes.

In languages without explicit support, protocols are often still present as conventions. This is known as duck typing. For example, in Python, any class can implement an  method and be used as a collection.

Type classes in languages like Haskell, or module signatures in ML and OCaml, are used for many of the things that protocols are used for.

In Rust, interfaces are called traits.

title: Interface (object-oriented programming)


text:
Monarchy of Sweden

The monarchy of Sweden is centred on the monarchical head of state of Sweden, by law a constitutional and hereditary monarchy with a parliamentary system. There have been kings in what now is the Kingdom of Sweden for more than a millennium. Originally an elective monarchy, it became a hereditary monarchy in the 16th century during the reign of Gustav Vasa, though virtually all monarchs before that belonged to a limited and small number of political families which are considered to be the royal dynasties of Sweden.

The official continuous count usually begins with the kings who ruled both Svealand and Götaland as one kingdom. Sweden's monarchy is amongst the oldest in the world, with a regnal list stretching back to the tenth century, starting with Eric the Victorious; the Swedish monarchy has, for the past thousand years, undergone cycles of decline and strengthening, culminating in the modern constitutional monarchy.

The Swedish monarchy has been one of the key features in the development of Swedish culture, having for centuries patronized the arts and sciences. Several of Sweden's most prestigious academies and cultural institutions are under Swedish royal protection. This historical role politically, militarily and culturally, in spite of the country's otherwise liberal leanings, has resulted in the Swedish monarchy being popular. In recent years, however, some of the most serious criticism ever published has taken place about the way his monarchy has developed under the current king's fifty-year reign.

Sweden in the present day is a representative democracy in a parliamentary system based on popular sovereignty, as defined in the current Instrument of Government (one of the four Basic Laws of the Realm which makes up the written constitution ). The monarch and the members of the royal family undertake a variety of official, unofficial and other representational duties within Sweden and abroad. The current king of Sweden is Carl XVI Gustaf, while his heir is Crown Princess Victoria.

The Swedish monarch has numerous residences, primarily state-owned but some privately owned; their official residence and workplace is Stockholm Palace, while Drottningholm Palace serves as the monarchy's private residence. Other notable residences include Gripsholm Castle and Ulriksdal Palace, as well as others throughout Sweden. Several large palaces and a considerable section of the Swedish capital of Stockholm have been at the disposal of the monarch since 1809.

Pre-16th century

Scandinavian peoples have had kings since prehistoric times. As early as the 1st century CE, Tacitus wrote that the Suiones had a king, but the order of Swedish regnal succession up until King Eric the Victorious (died 995), is known almost exclusively through accounts in historically controversial Norse sagas (see Mythical kings of Sweden and Semi-legendary kings of Sweden).

Originally, the Swedish king had combined powers limited to that of a war chief, a judge and a priest at the Temple at Uppsala (see Germanic king). However, there are thousands of runestones commemorating commoners, but no known chronicle about the Swedish kings prior to the 14th century (though a list of kings was added in the Westrogothic law), and there is a relatively small number of runestones that are thought to mention kings: Gs 11 (Emund the Old – reigned 1050–1060), U 11 (Håkan the Red – late 11th century) and U 861 (Blot-Sweyn – reigned c. 1080).

About 1000 A.D., the first king known to rule both Svealand and Götaland was Olof Skötkonung, but further history for the next two centuries is obscure, with many kings whose tenures and actual influence/power remains unclear. The Royal Court of Sweden, however, does count Olof's father, Eric the Victorious, as Sweden's first king. The power of the king was greatly strengthened by the introduction of Christianity during the 11th century, and the following centuries saw a process of consolidation of power into the hands of the king. The Swedes traditionally elected a king from a favored dynasty at the Stones of Mora, and the people had the right to elect the king as well as to depose him. The ceremonial stones were destroyed around 1515.

In the 12th century, the consolidation of Sweden was still affected by dynastic struggles between the Erik and Sverker clans, which ended when a third clan married into the Erik clan and the House of Bjelbo was established on the throne. That dynasty formed pre-Kalmar Union Sweden into a strong state, and finally king Magnus IV (reigned 1319–1364) even ruled Norway (1319–1343) and Scania (1332–1360). Following the Black Death, the union weakened, and Scania reunited with Denmark.

In 1397, after the Black Death and domestic power struggles, Queen Margaret I of Denmark united Sweden (then including Finland), Denmark and Norway (then including Iceland) in the Union of Kalmar with the approval of the Swedish nobility. Continual tension within each country and the union led to open conflict between the Swedes and the Danes in the 15th century. The union's final disintegration in the early 16th century led to prolonged rivalry between Denmark-Norway and Sweden (with Finland) for centuries to come.

16th- and 17th-century changes

Catholic bishops had supported the King of Denmark, Christian II, but he was overthrown in a rebellion led by nobleman Gustav Vasa, whose father had been executed at the Stockholm bloodbath. Gustav Vasa (hereinafter referred to as Gustav I) was elected King of Sweden by the Estates of the Realm, assembled in Strängnäs on 6 June 1523.

Inspired by the teachings of Martin Luther, Gustav I used the Protestant Reformation to curb the power of the Roman Catholic Church. In 1527 he persuaded the Estates of the Realm, assembled in the city of Västerås, to confiscate church lands, which comprised 21% of the country's farmland. At the same time, he broke with the papacy and established a reformed state church: the Church of Sweden. Throughout his reign, Gustav I suppressed both aristocratic and peasant opposition to his ecclesiastical policies and efforts at centralisation, which to some extent laid the foundation for the modern Swedish unitary state. Legally Sweden has only been a hereditary monarchy since 1544 when the Riksdag of the Estates, through Västerås arvförening, designated the sons of King Gustav I as the heirs to the Throne.

Tax reforms took place in 1538 and 1558, whereby multiple complex taxes on independent farmers were simplified and standardised throughout the district and tax assessments per farm were adjusted to reflect ability to pay. Crown tax revenues increased, but more importantly the new system was perceived as fairer. A war with Lübeck in 1535 resulted in the expulsion of the Hanseatic traders, who previously had had a monopoly on foreign trade. With its own burghers in charge, Sweden's economic strength grew rapidly, and by 1544 Gustav controlled 60% of the farmlands in all of Sweden. Sweden now built the first modern army in Europe, supported by a sophisticated tax system and an efficient bureaucracy.

At the death of King Gustav I in 1560, he was succeeded by his oldest son Eric XIV. His reign was marked by Sweden's entrance into the Livonian War and the Northern Seven Years' War. The combination of Eric's developing mental disorder and his opposition to the aristocracy led to the Sture Murders in 1567 and the imprisonment of his brother John (III), who was married to Catherine Jagiellon, sister of King Sigismund II of Poland. In 1568 Eric was dethroned and succeeded by John III. In domestic politics John III showed clear Catholic sympathies, inspired by his queen, creating friction with the Swedish clergy and nobility. He reintroduced several Catholic traditions previously abolished, and his foreign policy was affected by his family connection to the Polish–Lithuanian Commonwealth, where his eldest son had been made King Sigismund III in 1587. Following the death of his father, Sigismund tried to rule Sweden from Poland, leaving Sweden under the control of a regent – his paternal uncle (Gustav I's youngest son) Charles (IX) – but was unable to defend his Swedish throne against the ambitions of his uncle. In 1598 Sigismund and his Swedish-Polish army were defeated at the Battle of Stångebro by the forces of Charles, and he was declared deposed by the Estates in 1599.

In 1604, the Estates finally recognized the regent and de facto ruler as King Charles IX. His short reign was one of uninterrupted warfare. The hostility of Poland and the breakup of Russia involved him in overseas contests for the possession of Livonia and Ingria, the Polish–Swedish War (1600–1611) and the Ingrian War, while his pretensions to claim Lapland brought on a war with Denmark (Kalmar War) in the last year of his reign.

Gustavus Adolphus inherited three wars from his father when he ascended to the throne. From 1612, when Count Axel Oxenstierna was appointed Lord High Chancellor, which he remained until Gustavus Adolphus's death, the two men struck a long and successful partnership and complemented each other well: In Oxenstierna's own words, his "cool" balanced the King's "heat". The war against Russia (the Ingrian War) ended in 1617 with the Treaty of Stolbovo, which excluded Russia from the Baltic Sea. The final inherited war, the war against Poland, ended in 1629 with the Truce of Altmark, which transferred the large province of Livonia to Sweden and freed the Swedish forces for subsequent intervention in the Thirty Years' War in Germany, where Swedish forces had already established a bridgehead in 1628. Brandenburg was torn apart by a quarrel between the Protestants and the Catholics. When Gustavus Adolphus began his push into northern Germany in June–July 1630, he had just 4,000 soldiers. But he was soon able to consolidate the Protestant position in the north, using reinforcements from Sweden and money supplied by France at the Treaty of Bärwalde. Gustavus Adolphus was killed at the 1632 Battle of Lützen. Queen Maria Eleonora and the king's ministers took over the government of the Realm on behalf of Gustavus Adolphus' underage daughter Christina, until she reached the age of majority. Gustavus Adolphus is often regarded by military historians as one of the greatest military commanders of all time, with innovative use of combined arms.

As the heiress presumptive, at the age of six Christina succeeded her father on the Swedish throne (being the only person left in the line of succession), although a regency government would rule in her name until she turned 18 years of age. During the regency, Chancellor Axel Oxenstierna wrote the 1634 Instrument of Government, which although never approved by any monarch, nevertheless would continue to have an important normative role in the state administration. Christina early on showed an interest in literature and the sciences and famously brought René Descartes to Sweden. Sweden continued to be involved in the Thirty Years' War during reign of Christina and that conflict was settled at the 1648 Peace of Westphalia, and the Swedish monarch received representation at the Imperial Diet due to the German conquests (Bremen-Verden and Swedish Pomerania) that were made. Having decided not to marry, Christina abdicated the throne on 5 June 1654 in favor of her cousin Charles Gustav, went abroad, and converted to Roman Catholicism.

The Estates elected Charles X Gustav as their new King, and his short reign is best characterized by foreign wars: first a lengthy campaign within Poland and then with Denmark. In the latter case, the risky 1658 March across the Belts which resulted in the Treaty of Roskilde, would prove to be the largest permanent territorial gain Sweden ever had: Skåne, Blekinge and Bohuslän now became Swedish provinces and have remained so ever since. Charles X Gustav was not satisfied, as he wanted to crush Denmark once and for all, but the 1659 Assault on Copenhagen did not prove successful for the Swedes, largely due to the Dutch naval intervention to the aid of the Danes.

Charles X Gustav died in Gothenburg in 1660 and as the Crown passed to his five-year-old son Charles XI, a new regency government would assume the responsibilities of the state. The regency government, composed of aristocrats and led by Chancellor Count Magnus Gabriel De la Gardie, was more interested in feathering their own nests rather than working in the interest of the country at large. When Charles XI came of age in 1672, the effectiveness of the armed forces had seriously deteriorated and the country was ill-prepared as the King of Denmark, Christian V, invaded to settle old scores. The Danes were ultimately unsuccessful in their attempts, and Charles XI undertook several measures to prevent what had just almost happened from occurring again: reducing the influence of the aristocracy by nationalizing estates and properties which had been handed out to them by his predecessors, introducing the Allotment system (indelningsverket) which would form the basis of the armed forces until the 20th century, and with the support of the Estates he was declared in 1680 an absolute monarch.

Charles XI was succeeded by his son, Charles XII, who would prove to be an extremely able military commander, defeating far larger enemies with the small but highly professional Swedish army. His defeat of the Russians at Narva when just 18 years old was to be his greatest victory. However his campaigning at the head of his army during the Great Northern War would ultimately lead to catastrophic defeat at the Battle of Poltava after which he spent several years in Turkey (now Moldova). Some years later he was killed at the Siege of Fredriksten during an attempt to invade Norway. The Swedish Age of Greatness (stormaktstiden) had ended.

18th century to the present
Charles XII's sister, Ulrika Eleonora, now claimed the throne over her nephew and son of her elder sister, Charles Frederick, Duke of Holstein-Gottorp (see genealogy chart above). Charles Frederick had the claim of seniority within the family, but Ulrica Eleonora claimed that her elder sister had not "acquired the consent of the Parliamentary Estates" for her marriage to his father, according to laws of succession laid down in Norrköpings arvförening. The duke's party asserted that the absolute monarchy in Sweden, which his grandfather King Charles XI had created, made that marriage clause irrelevant. When Charles Frederick was confronted with Ulrika Eleonora, he was forced by Arvid Horn to greet her as queen. He asked to be granted the title Royal Highness and to be recognised as her heir, but when her husband, Frederick of Hesse, instead was given the title, he left Sweden in 1719. In 1723, he was granted the title Royal Highness in his absence, but his pro-Russian policy at that time made him impossible as heir to the Swedish throne. His marriage in 1725 to Anna, the daughter of Peter of Great, did not help his case. His mother, and later Hedwig Eleonora, both supported and worked for his right to be considered heir of Sweden after his childless uncle.

Ulrika Eleonora was forced by the Estates to sign the 1719 Instrument of Government, which ended the absolute monarchy and made the Riksdag of the Estates the highest organ of the state and reduced the role of monarch to a figurehead. The Age of Liberty (frihetstiden) with its parliamentary rule, dominated by two parties – the Caps and the Hats – had begun. Ulrika Eleonora had had enough after a year on the throne and abdicated in favor of her husband, Frederick, who had little interest in the affairs of state and was elected King by the Estates as King Frederick I, resulting in the 1720 Instrument of Government: content-wise almost identical to the one from 1719. Despite having many extra-marital affairs, Frederick I never sired a legitimate heir to the throne.

who had adopted his nephew as her heir. On his mother's side, Adolf Frederick was descended from King Gustav Vasa and Christina Magdalena, a sister of Charles X of Sweden. He succeeded as King Adolf Frederick 8 years later on 25 March 1751.

During his 20-year reign, Adolf Frederick was little more than a figurehead, the real power being with the Riksdag of the Estates, often distracted by party strife. Twice he endeavored to free himself from the tutelage of the estates. The first occasion was in 1756. Stimulated by his consort Louisa Ulrika of Prussia (sister of Frederick the Great), he tried to regain a portion of the attenuated prerogative through the Coup of 1756 to abolish the rule of the Riksdag of the Estates and reinstate absolute monarchy in Sweden. He nearly lost his throne in consequence. On the second occasion during the December Crisis of 1768, under the guidance of his eldest son, Gustav, he succeeded in overthrowing the "Cap" (Swedish: Mössorna) senate, but was unable to make any use of his victory.

Adolf Frederick's son, King Gustav III, was more successful in restoring royal authority. In 1772, the 1720 Instrument in Government was later replaced by the 1772 Instrument of Government in a self-coup orchestrated by the King.

On 17 September 1809 in the Treaty of Fredrikshamn, as a result of the poorly managed Finnish War, Sweden had to surrender Finland to Russia. King Gustav IV Adolf and his descendants were deposed in a coup d'état led by dissatisfied army officers. The childless uncle of the former king was almost immediately elected as King Charles XIII. The Instrument of Government of 1809 put an end to royal absolutism by dividing the legislative power between the Riksdag (primary) and the king (secondary), and vested executive power in the king when acting through the Council of State.

The present Bernadotte dynasty was established in September 1810 when the Riksdag, convened in Örebro, elected French Marshal and Prince of Pontecorvo Jean-Baptiste Jules Bernadotte as crown prince. This took place because Charles XIII had no legitimate heir, and a crown prince previously elected in January 1810, Charles August, suddenly had died of a stroke during a military exercise.

Although the 19th century Bernadotte monarchs that would follow Charles XIV John's reign tried to defend the power and privileges they still had, the tide incrementally turned against "personal regal rule" (personlig kungamakt) with the growth of the liberals, social democrats, and the expansion of the franchise.

The daughter of Gustav IV Adolph, Princess Sofia Wilhelmina (21 May 1801 – 1865) married Grand Duke Leopold of Baden, and their granddaughter Victoria of Baden married the Bernadotte king Gustaf V of Sweden. The present King Carl XVI Gustaf of Sweden is thus Gustav IV's heir through his grandfather, Gustav VI Adolf.

When King Gustav V publicly objected to the defence budget cuts made by Prime Minister Karl Staaff and the cabinet just before the First World War in event known as the Courtyard Crisis accompanied by the Peasant armament support march (bondetåget), it was seen as a deliberate provocation by conservatives and reactionaries against the uncodified norm of a parliamentary system supported by the liberals and the social democrats, leading to Staaff's resignation. Gustaf V then appointed a caretaker government, supported by the conservatives, led by legal scholar Hjalmar Hammarskjöld, which remained in power longer than expected due to the outbreak of World War I (in which Sweden remained neutral) and increased defence spending was no longer a controversial issue. Nevertheless, in the year of the outbreak of the Russian Revolution, social tensions continued to rise; the general election in 1917 gave the liberals and social democrats greatly strengthened representation in both Riksdag chambers and a conservative government was no longer a defensible option. Following the definite breakthrough of parliamentarism in 1917, with the appointment of the coalition government of liberals and social democrats led by professor Nils Edén, the political influence of the King was considerably reduced and an unwritten constitutional precedent was set that would remain in effect until 1975.

Only during World War II, in the so-called Midsummer crisis (regarding the issue whether neutral Sweden should permit rail transport of German troops from Norway passing through to Finland), did Gustaf V allegedly try to intervene in the political process by threatening to abdicate.

King Gustaf VI Adolf succeeded his elderly father who died in 1950, and he is generally regarded as a constitutional monarch who stayed out of politics and controversy. In 1954, a royal commission began work on whether Sweden should undergo constitutional reform to adapt the 1809 Instrument of Government to current political realities, or whether a new one should be written; ultimately the latter idea was chosen. The future role of the monarchy was settled in a manner well known within Swedish political discourse: a political compromise reached at the summer resort of Torekov in 1971 (hence known as the Torekov compromise, Torekovskompromissen) by representatives of four of the parties in the Riksdag (the Social Democrats, the Centre Party, the Liberal People's Party, and the Moderate Party, that is all the parties except the Communists). It mandated that the monarchy would remain largely as it was but would become entirely ceremonial, without any residual political powers left.

Following the required double Riksdag votes that took place in 1973 and 1974, a new Instrument of Government was brought into effect. The monarch's functions and duties, as defined in the 1974 Constitution Act, include heading the special cabinet council held when there is a change of government, but no executive powers with respect to the governance of the realm are vested in him.

Carl XVI Gustaf became king on 15 September 1973 on the death of his grandfather Gustaf VI Adolf and because of his father's early death has become the longest reigning monarch in Swedish history. His King's Golden Jubilee was celebrated in 2023. Leading up to that year and including it, beginning already in 2018, some of the most serious criticism ever published took place about Carl Gustaf and the way the monarchy has developed during his reign.

Constitutional and official role
When, on 1 January 1975, it replaced the Instrument of Government of 1809 as part of the Constitution of Sweden, the Instrument of Government of 1974 (1974 års regeringsform) transformed the advisory Council of State (Statsrådet) into the collegial Government (Regeringen), to which all executive power was transferred. Responsibility for nominating and dismissing the prime minister (who, since 1975, is elected by the Riksdag) was transferred to the Speaker of the Riksdag; the prime minister appoints and dismisses the other ministers at his or her discretion. Furthermore, bills passed by the Riksdag become law without royal assent: the prime minister or any other cabinet minister signs them "On Behalf of the Government" (På regeringens vägnar).

Although the unwritten precedent was set in 1917, when Gustaf V had little choice but to support the idea of a parliamentary system and promised Prime Minister Nils Edén to stop seeking advice from secret advisors other than the duly appointed cabinet ministers and not to interfere in politics again; the Torekov compromise, struck in 1971 by the four major parties at the time, provided, and continues to provide, a majority consensus in Swedish political discourse on the role of the monarchy within the constitutional framework. The official motive for the radical changes which came to pass in 1975 was for it to be as descriptive as possible of the workings of the state and clear on how decisions actually are made. Minister of Justice Lennart Geijer further remarked on the 1973 government bill that any continued pretensions of royal involvement in government decision making would be of a "fictitious nature" and therefore "highly unsatisfactory".

Thus, the monarch lost all formal executive powers, becoming a ceremonial and representative figurehead. The monarch, while explicitly referred to as the "Head of State" (Statschefen) in the 1974 Instrument of Government, is not even the nominal chief executive. The Instrument of Government of 1974 does grant the person serving as king or queen regnant absolute immunity from criminal (but not civil) charges for as long as he or she remains in office. The monarch therefore cannot be prosecuted or otherwise held to account for his or her actions, both official and private, in judicial proceedings. None of the other members of the royal family or the employees the Royal Court enjoy similar immunity.

At the request of the Speaker of the Riksdag, the monarch opens the annual session of the Riksdag (Riksmötets öppnande) in the chamber of the Riksdag building. The king or queen regnant also receives Letters of Credence of foreign ambassadors sent to Sweden and signs those of Swedish ambassadors sent abroad. The monarch also chairs the Cabinet Council (skifteskonselj) in a session that establishes the new government following a general election or major cabinet reshuffle and also chairs information councils (informationskonselj) approximately four times a year to get information from the assembled Government, apart from that given by ministers in individual audiences or through other means. Formally, it is the explicit responsibility of the prime minister to keep the monarch informed on the affairs of the realm; the failure to do so following the 2004 tsunami disaster in the Indian Ocean (in which many Swedes perished) gave rise to wide criticism of Prime Minister Göran Persson for his handling of the matter. The monarch also chairs the Advisory Council on Foreign Affairs (Utrikesnämnden), a body that enables the government of the day to inform not only the head of state, but also the speaker and representatives of the opposition parties in the Riksdag, on foreign affairs issues in a confidential manner.

While the monarch is no longer the commander-in-chief (högste befälhavare) of the Swedish Armed Forces, as he once was under the 1809 Instrument of Government King Carl XVI Gustaf is the foremost representative of the Swedish defence establishment and holds supreme rank in each of the service arms. He ranks as a four star admiral in the Swedish Navy and general in the Swedish Army and Air Force. As part of his court, the monarch has a military staff, which is headed by a senior officer (usually a general or admiral, retired from active service) and includes active duty military officers serving as aides-de-camp to the monarch and his or her family.

Cultural role
The monarch and members of the Royal Family undertake a variety of official, unofficial and other representative duties within Sweden and abroad. The monarch and his or her family play a central role in state visits to Sweden and conduct state visits to other nations on behalf of Sweden. Other members of the Royal Family may also represent the country abroad at lesser functions.

Many of the Swedish general flag flying days have direct royal connections; among them are the name days of the King (28 January), the Queen (8 August), and the Crown Princess (12 March); the birthdays of the King (30 April), the Queen (23 December), and the Crown Princess (14 July); and Gustavus Adolphus Day (Gustav Adolfsdagen), on 6 November, in memory of King Gustavus Adolphus, who was killed on that date (old style) in 1632 in the Battle of Lützen. None of these flag days are public holidays, however.

Perhaps the most globally known ceremony in which the Royal Family annually participate is the Nobel Prize award ceremony held at the Stockholm Concert Hall (and the subsequent banquet in the Stockholm City Hall), where the monarch hands out the Nobel Prizes on behalf of the Nobel Foundation for outstanding contributions to mankind in physics, chemistry, literature, physiology or medicine, and the economic sciences.

Eriksgata was the name of the traditional journey of newly elected medieval Swedish kings through important provinces to have their election confirmed by local Things. The actual election took place at the Stone of Mora in Uppland and participation was originally restricted to the people of that area; hence, the need of having the election confirmed by the other parts of the realm. The Eriksgata gradually lost its importance when, as of the 14th century, representatives of other parts of Sweden began to participate in the election. After 1544, when hereditary monarchy was instituted, that meant that the Eriksgata had little practical importance. The last king to travel the Eriksgata according to the old tradition was Charles IX, whose reign began in 1604. Later, kings, up until present times, have made visits to all the Swedish provinces and called them an Eriksgata, while those visits bear little resemblance to the medieval tradition.

Monarch
The full title of the Swedish monarch from 1523 to 1973 was:

":In Med Guds Nåde Sveriges, Götes och Vendes Konung
 * In Dei Gratia Suecorum, Gothorum et Vandalorum Rex

Translated as 'By the Grace of God, King of the Swedes, the Goths, and the Wends' or 'By the Grace of God, King of Sweden, of the Goths and Vandals'."

During the reign of the House of Holstein-Gottorp from 1751 to 1818, the title Heir to Norway (Arvinge till Norge) was also used, as well as other titles connected to the Dukes of Holstein-Gottorp. When, after the Napoleonic Wars, Norway was in personal union with Sweden, the title included King of Norway, in older Swedish spellings: Sweriges, Norriges, Göthes och Wendes Konung.

Upon his accession, Carl XVI Gustaf chose for his title simply Sveriges Konung (King of Sweden).

Dynasts
The customary title of the heir apparent is crown prince (kronprins) or crown princess (kronprinsessa). The wife of a crown prince would also receive a corresponding title, but not the husband of a crown princess. The traditional official title used until 1980 for other dynastic male heirs was hereditary prince (arvfurste), although the word prince (prins) was used in constitutional legal texts such as the Act of Succession and also colloquially and informally. Female dynasts are titled princess (prinsessa).

The Swedish Succession Act was altered in 1980 to allow for female succession to the throne.

Ducal titles
King Gustav III revived a tradition from the time of Gustav Vasa and the medieval era by giving male heirs to the throne ducal titles of Swedish provinces. The difference between the ducal titles from the Vasa era and those granted by Gustav III is they now are non-hereditary courtesy titles given at birth. Since 1980, they have been conferred to all royal heirs, male and female. The wives of royal dukes have always shared their husbands' titles; the husbands of royal duchesses have done so as of 2010.

Regalia

The regalia of Sweden are kept deep in the vaults of the Treasury of Sweden (Skattkammaren), located underneath the Royal Palace in Stockholm, in a museum which has been open to the public since 1970. Among the oldest objects in the collection are the sword of Gustav Vasa and the crown, orb, sceptre and key of King Erik XIV. The Regalia is state property and the government authority which holds it in trust is the Legal, Financial and Administrative Services Agency.

The last king to have been crowned was Oscar II. His son and successor, Gustaf V, abstained from having a coronation. While the crowns and coronets have not been worn by Swedish royalty since 1907, they are nevertheless still displayed on royal occasions such as at weddings, christenings and funerals. Until 1974, the crown and sceptre were also displayed on cushions beside the Silver Throne at the annual solemn opening of the Riksdag (Riksdagens högtidliga öppnande).

Royal orders of chivalry
The Royal orders have a historical basis, dating back to the 1606 founding of the now extinct Jehova Order. The Royal Orders of Knights of Sweden were only truly codified in the 18th century, with their formal foundation in 1748 by King Frederick I. In 1974 the Riksdag significantly changed the conditions and criteria under which orders and decorations could be awarded: that no Swedish citizen outside the Royal Family is eligible to receive such decorations. The Order of the Seraphim (Serafimerorden) is only awarded to foreign heads of state and members of the Swedish and foreign royal families, while the Order of the Polar Star (Nordstjärneorden) was only to be bestowed on any non-Swedish citizen. Following the reforms, the Order of the Sword (Svärdsorden) and the Order of Vasa (Vasaorden) were no longer conferred: officially they were declared as "dormant". In 2022 the government proposed a new reform taking effect in 2023 that once again opened the Royal Orders so that they now may be awarded to Swedish citizens again. The Order of the Seraphim however was not affected by these changes.

Between 1975 and 2023, H. M. The King's Medal (H.M. Konungens medalj) was the highest honour that could be awarded to Swedish citizens other than members of the Royal Family.

Royal residences
The Royal Palaces (including the Royal Palace in Stockholm, Drottningholm Palace, Haga Palace, Rosendal Palace, Ulriksdal Palace, Rosersberg Palace, Tullgarn Palace and Gripsholm Castle) are government property, managed by the National Property Board (Statens fastighetsverk) and are at the disposal of the Monarch, an arrangement that has been in place since the beginning of the 19th century. There are also residences which are held privately by the Royal Family, such as Solliden Palace on the island of Öland, a cottage in Storlien in the Jämtland and Villa Mirage in Sainte-Maxime in southern France (originally acquired by Prince Bertil).

Royal Palace
The Royal Palace (Kungliga slottet), also known as Stockholm Palace (Stockholms slott), is the official residence of the king. The Royal Palace is located on Stadsholmen ("City Island"), commonly known as Gamla Stan ("the Old Town") in the national capital city Stockholm.

The offices of the king, other members of the Swedish Royal Family, and the offices of the Royal Court are located in the palace. The Royal Palace is used for representative purposes and State occasions by the king. The Royal Palace is guarded by Högvakten, a royal guard, consisting of regular service members of the Swedish Armed Forces. The tradition of having a regular unit of the Army guarding at the royal residence dates back to 1523. Until the mid-19th century, the royal guards also maintained law and order in the city and provided firefighting services.

The southern façade faces the grand style slope Slottsbacken; the eastern façade borders Skeppsbron, a quay which passes along the eastern waterfront of the old town; on the northern front Lejonbacken is a system of ramps named for the Medici lions, sculptures on the stone railings; and the western wings border the open space Högvaktsterrassen. The Royal Palace in Stockholm is unique among European royal residences in that large portions of it are open year-round to visitors, who pay entrance fees.

The first building on this site was a fortress with a keep built in the 13th century by Birger Jarl to defend the entry into Lake Mälaren. The fortress gradually grew to a castle, known as Tre Kronor: named after the spire on the centre tower with Three Crowns, which have become the Swedish national symbol. In the late 16th century, work was done to transform the castle into a Renaissance palace during the reign of John III. In 1690, it was decided that the castle be rebuilt in Baroque style in a design by Nicodemus Tessin the Younger. In 1692, work began on the northern row. However, much of the old castle was destroyed in a disastrous fire on 7 May 1697.

Tessin rebuilt the damaged palace, and work continued for another 63 years. Semicircular wings around the outer western courtyard were finished in 1734, the palace church was finished in the 1740s, and the exterior was finished in 1754. The royal family moved to the palace with the southwest, southeast, and northeast wings finished. The northwest wing was finished in 1760. In the north, Lejonbacken (the "Lion's Slope") was rebuilt from 1824 to 1830.

Drottningholm Palace
Drottningholm Palace (Drottningholms slott) is located at Drottningholm on the island of Lovön (in Ekerö Municipality of Stockholm County), and is one of Sweden's Royal Palaces. It was originally built in the late 16th century. It has served as a residence of the Swedish royal family members for most of the 18th and 19th centuries. Apart from being the current private residence of the King and Queen, Drottningholm Palace is a popular tourist attraction.

The gardens and park areas surrounding Drottningholm Palace and adjacent to its buildings are one of the main attractions for the tourists that visit the palace each year. The gardens have been established in stages since the palace was first built, resulting in many different styles.

The royal domain of Drottningholm is a well-preserved milieu from the 17th and 18th centuries, inspired by French buildings such as the Chateau of Versailles, and is a UNESCO World Heritage Site, principally because of the Drottningholm Palace Theatre and the Chinese Pavilion at Drottningholm. It was added to the World Heritage List in 1991.

Haga Palace
Haga Palace (Haga slott), formerly known as the Queen's Pavilion (Drottningens paviljong), is located in the Haga Park, Solna Municipality in Metropolitan Stockholm. The palace, built between 1802 – 1805, was modelled after balletmaster Louis Gallodier's Italian villa at Drottningholm by architect Carl Christoffer Gjörwell on appointment by King Gustaf IV Adolf for the royal children. It has been the home or summer house of several members of the Swedish royal family – notably it was the birthplace of the present King Carl XVI Gustaf – until 1966 when King Gustaf VI Adolf transferred its disposal to the prime minister and it was turned into a guest house for distinguished foreign official visitors (heads of state and heads of government et cetera).

In April 2009, it was announced by Prime Minister Fredrik Reinfeldt that the rights of disposal of the palace would be transferred back to the King and thus could be used by Crown Princess Victoria and her husband, Prince Daniel, Duke of Västergötland. They moved into the palace in the autumn after their wedding on 19 June 2010.

Royal Family
The Swedish royal family is, according to the Royal Court, currently categorized into three groups;
 * first, those with royal titles and style (manner of address) who perform official and unofficial engagements for the nation, are the members of the Royal Family (Kungafamiljen) (currently this category only includes the King, Queen and their descendants, including spouses);
 * second, those with royal titles and style (manner of address) who perform no official engagements (Kungliga Huset, usually stylized with the shortform Kungl. Huset);
 * and third, the extended family of the King (Kungliga Familjens övriga medlemmar, usually stylized with the shortform Kungl. Familjens övriga medlemmar) which is other close relatives who are not dynasts and thus do not represent the country officially.

However, in any case, there is no legislation or other public document which delineates the rules of membership in either the Royal House or Royal Family, as it is left to the sole discretion of the King.

The line of succession

The Act of Succession of 1810 provides the rules governing the line of succession and designates the legitimate heirs to the Swedish Throne; it also states in article 4 that the Monarch and dynastic members of the Royal House must at all times be a Protestant Christian of the pure evangelical faith (by implication the Church of Sweden).

A rewrite of the Act, entering into force in 1980, fundamentally changed the rules of succession from agnatic primogeniture to absolute primogeniture. This allowed for the crown to pass to the eldest child regardless of gender and thus retroactively installed Princess Victoria as crown princess over her younger brother, Prince Carl Philip, who had been born as crown prince a few months before.

In its present reading, Article 1 of the Act of Succession limits the potential number of claimants to the throne, so that only the descendants of Carl XVI Gustaf can inherit the Throne. If the royal house were to be extinct, the Riksdag is not obligated to elect a new royal house, as it once was up until the constitutional reforms of the 1970s.

title: Monarchy of Sweden


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Parabolic microphone

A parabolic microphone is a microphone that uses a parabolic reflector to collect and focus sound waves onto a transducer, in much the same way that a parabolic antenna (e.g. satellite dish) does with radio waves. Though they lack high fidelity, parabolic microphones have great sensitivity to sounds coming from one direction, along the axis of the dish, and can pick up distant sounds.

Limitations
Parabolic microphones are generally not used for high fidelity applications because dishes small enough to be portable have poor low-frequency response. This is because, from the Rayleigh criterion, parabolic dishes can only focus waves with a wavelength much smaller than the diameter of their aperture. The wavelength of sound waves at the low end of human hearing (20 Hz) is about 17 metres; focusing them would require a dish much larger than this. A typical parabolic microphone dish with a diameter of one metre has little directivity for sound waves longer than 30 cm, corresponding to frequencies below 1 kHz. For higher frequencies, a gain of about 15 dB can be expected. But when the wavelength of the sound becomes comparable with the diameter of the parabolic dish, the response falls away.

A shotgun microphone, or a phased array of microphones, may be used as an alternative for applications requiring directional selectivity with high fidelity.

Applications
Typical uses of this microphone include nature sound recording such as recording bird calls, field audio for sports broadcasting, and eavesdropping on conversations, for example in espionage and law enforcement. Parabolic microphones were used in many parts of the world as early as World War II, especially by the Japanese.

Parabolic microphones are also used by search and rescue teams to locate lost people in wilderness environments. This application is supported by a study comparing parabolic microphones to unaided hearing in detecting and comprehending calling subjects at distances out to 2500 meters.

title: Parabolic microphone