# Tagged Questions

The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

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### Energy of classical ideal gas in the grand canonical ensemble

The canonical partition function for an ideal gas is $Z(N,V,\beta) = \frac{1}{N!} (\frac{V}{\lambda^3})^N$ where $\lambda = \sqrt{\frac{\beta h^2}{2 \pi m}}$ is the thermal De-Broglie wavelength. It ...
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### Decoherence in the long time limit of density matrix elements

For a state $$|\Psi(t)\rangle = \sum_{k}c_k e^{-iE_kt/\hbar}|E_k\rangle,$$ the density matrix elements in the energy basis are $$\rho_{ab}(t) = c_a c^*_be^{-it(E_a -E_b)/\hbar}$$ How is it that ...
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### RMS Speed of Gas Molecule for Polyatomic Molecules

Halliday in his book and also many people say that RMS speed, $v_{rms}$ is $\sqrt{\frac{3RT}{M}}$. However, he used this formula in showing that kinetic energy, $K$, is $\frac32kT$. but how about ...
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### Temperature of system in canonical ensemble

Upon reading Reif's explanations relating to systems exchanging energy and the canonical ensemble (Reif, Fundamentals of statistical and thermal physics, p. 95ff and p. 202ff), I am led to conclude ...
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### On the surface, is the law of maximum entropy production the same as principle of least action?

I just have read about the law of maximum entropy production. Someone has idolized it enough to make an whole website just for it: http://www.lawofmaximumentropyproduction.com/ A system will ...
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### Probability in canonical ensemble - relation to temperature

I've got a conceptual question about the canonical ensemble. In the derivation of the probability distribution (see e.g. Kardar, Statistical physics of particles, p. 110ff) it is stated that a small ...
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### Is the wavefunction of particles inside a gas spread or localized?

For an individual free particle that starts localized, the wave function packet spreads over time, so the particle becomes less localized. Suppose now that we have a gas of those particles inside a ...
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### Which quasiparticles follow which statistics [closed]

Let me say beforehand that I know this is an ill-defined question, but I believe it is useful anyway. For these common quasiparticles: Phonons Holes Plasmons Excitons Plasmon-polaritons What ...
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### Does gravity acting on a resting object produce any heat?

Let's compare two systems. System 1: A box is completely isolated. There are no forces acting on that object, and no interactions of any kind with other objects, waves, etc.. System 2: The same box ...
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### What is the cause for the inclusion of 'thermal equilibrium' in the statement of Ergodic hypothesis?

This is the fundamental assumption of statistical mechanics: In an isolated system in thermal equilibrium $^1$, all accessible microstates are equally probable. But why does it mention the ...
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### Does nucleation depend on the rate of change in pressure in a carbonated liquid?

Carbonated beer flowing from a keg through a short length of tubing results in large quantities of foam. Unintuitively (at least to me), increasing the length of tubing results in a less frothy drink. ...
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### What is the motivation behind defining short range order the way it is defined in Braggs-William approximation?

I am reading Statistical Mechanics by Kerson Huang. In the chapter on Ising model, it defines short range order as $\frac{2 N^{++}}{\gamma N}$ where $N^{++}$ is total number of spin up neighbours of ...
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### What is the correct relativistic distribution function?

General Statement and Questions I am trying to figure out the proper way to model a velocity/momentum distribution function that is correct in the relativistic limit. I would like to determine/know ...
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### temperature from a molecular point of view

The electric fan increases the velocity and hence the kinetic energy of the molecules in the air. this would mean that the temperature has increased. What's wrong with a conclusion? I want you to ...