Questions tagged [statistical-mechanics]
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23 questions
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When did the name “Boltzmann constant” prevail, and how?
This question is prompted by (comments at) another one. There, I was surprised to find that despite traditional claims to the contrary, Boltzmann himself did once write his formula $S=k\log W$:
$\...
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Did Democritus predict atoms using sharp phase transitions
In the Wikipedia page for the Ising Model it is written without citations:
One of Democritus' arguments in support of atomism was that atoms
naturally explain the sharp phase boundaries observed in
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What became of the Boltzmann-Zermelo debate about the second law of thermodynamics?
At the end of 19th century there was a lively discussion about the nature of the second law of thermodynamics, and its relation to Hamiltonian dynamics. Boltzmann developed a position that the second ...
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Who introduced the partition function?
Is it by Gibbs? Or Boltzmann? I do not expect Maxwell. The point is, how was the textbook introduction of partition function today developed.
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What is the origin of the name "degeneracy" pressure and "degenerate" Fermi gas?
What is the origin of the name "degeneracy" pressure and "degenerate" Fermi gas?
I was trying to find the first paper that used the term "degenerate/degeneracy" to ...
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Einstein's Objection to Drude Model
In Walter Isaacson's Biography of Einstein, it is stated that the young Einstein was developing his own ideas in Statistical Physics and Thermodynamics and he had found some error in Drude's model for ...
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What was Boltzmann's contribution to the theory of "statistical ensemble"?
In the book "Ludwig Boltzmann, the man who trusted atoms"by C.Cercignani, I read about the thesis according to which it was Boltzmann, not Gibbs who first introduced the concept of "...
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What is the difference between Einstein's and Boltzmann's definitions of probability?
In the Einstein's 1905 paper on light quanta, he wrote the following about Boltzmann's notion of probability:
The word probability is used in a sense that does not confirm to its definition as it ...
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Interpretation of $W$ in Boltzmann's entropy formula
Background
In the famous Boltzmann's entropy formula, carved in the physicist's tombstone, a mysterious quantity $W$ appears (a):
$$S=k_B \log W\label{1}\tag{1}$$
We often hear that $W$ represents "...
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Historical Survey of Statistical Mechanics
Statistical mechanics is a subject with a particularly rich history. I think of the early debates of Boltzmann and Loschmidt, the rather confusing differences between the approaches of Gibbs and ...
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Did Maxwell discover the distribution of velocities in a gas during an exam set by Stokes?
In some lecture notes I found online it was claimed that Maxwell discovered the Maxwell-Boltzmann distribution while in the course of solving a (then unsolved) examination problem given by Stokes. The ...
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What is the etymology of "phase space" of a dynamical system?
The state space of a dynamical system is often called a "phase space". What is the etymology of this?
(Note that I'm not asking about the history of the concept, but rather about the history of the ...
CommunityBot
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What did people understand heat and temperature to be in Clausius' time?
I just took a read of Clausius' original writing from 1867 on the second law. He refers to the "unit of heat" as "that amount of heat which is required to increase the temperature of unit-weight of ...
CommunityBot
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What were the dominant non-atomic theories of matter in the 19th century?
From what I have read, the atomic theory of matter was cemented by a 1905 paper by Einstein in which he explained the erratic motion of a bit of pollen suspended in water using the assumption that ...
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Why is the H theorem called the big Eta theorem?
In France, they refer to the H-theorem of Boltzmann (Théorème H) as 'eta'-theorem (théorème 'eta'). The connection obviously comes from the uppercase version of the Greek letter $\eta$, which looks ...
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Distinguishability of particles in statistical mechanics
Historically,how,and by what experiments,the concept of identical and distinguishable particles was discovered?Is it a tagline set by scientists,or nature indeed works in this way?
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Why are microcanonical, canonical and macrocanonical ensembles called that way?
In statistical mechanics, why microcanonical, canonical and macrocanonical ensemble are called that way?
Is there any reason according to the size of the system they can describe properly ( I don't ...
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History of XY model - Plane Rotator model
I would like to find out more about the history of the XY model. While for the Ising and Potts model it is easy to find information, it's quite difficult for me to understand when and where the XY ...
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Origin of diagrammatics illustrating the relation between cumulants and moments?
The exponential-log transformation of exponential generating functions (see OEIS A036040 and A127671) relate the classical cumulants to their associated moments.
Who were some of the first to ...
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Why are Bose-Einstein Condensates (BECs) named after Bose and Einstein?
Why are Bose-Einstein Condensates (BECs) named after Bose and Einstein? What did Einstein contribute to BECs?
Danu♦
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Who was the first to prove the Boltzman H-theorem for the Landau kinetic equation?
Who has proved Boltzmann's H-theorem (which tells that entropy of a closed system grows as the system approaches thermal equilibrium) for the kinetic equation with Landau collisions operator? One ...
CommunityBot
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Who was first to prove the Boltzman H-theorem for the Landau kinetic equation? [duplicate]
Who has proved Boltzmann's H-theorem (which tells that entropy of a closed system grows as the system approaches thermal equilibrium) for the kinetic equation with Landau collisions operator? One ...
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Who named the fugacity, who coined the variable name and did it already relate to complex analysis?
In Riemanns monumental paper, he expresses a prime counting function as an inverse Mellin transform of the log of the function he analytically continued into the complex plane
$$\Pi(x) = \frac{1}{2\...
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