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

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1answer
101 views

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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0answers
63 views

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 ...
3
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2answers
46 views

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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0answers
63 views

In an equilibrium of two systems, why is not true that $\frac{\delta S_{1}}{\delta N_{1}} = \frac{\delta S_{2}}{\delta N_{2}}$?

Why is not true that $\frac{\delta S_{1}}{\delta N_{1}} = \frac{\delta S_{2}}{\delta N_{2}}$ across two systems that exchange particles? It is true, instead, that $\frac{\delta F_{1}}{\delta N_{1}} = ...
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0answers
38 views

What creates multiplicity in counting the number of ways energy quanta can be distributed among a collection of atoms?

Say that I have $q$ energy quanta, which I intend to distribute among $N$ indistinguishable atoms in some collection. These atoms have no limit on the amount of quanta they can contain. Am I right ...
1
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1answer
125 views

Why is it so hard to explain that the Brownian Ratchet doesn't work?

The Brownian Ratchet stood up to a lot of scrutiny before it was finally shown why it would not work as a perpetual motion machine, but it seems weird to me that all of that was necessary. If the ...
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0answers
28 views

Explanation of example of ergodic movement

I was presented with the following question in as part of an introduction to ergodic movement: A man walks on a circle of radius 100 meters. Each man’s step is equal precisely 1 meter. There is a ...
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0answers
80 views

What is the meaning of thermal spectral function and thermal decay width in thermal field theory?

In Kallen-Lehmann spectral representation of 2-point correlation function \begin{equation} \langle 0|T\phi(x)\phi(0)|0\rangle=\int_0^\infty \frac{dM^2}{2\pi}\rho(M^2)D_F(x-y;M^2),\quad (a) \end{...
0
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1answer
88 views

Why is the number of distinct momentum states of a quantum particle moving in one dimension given as $\frac{L_p}{\Delta p_x}\;?$

I was reading multiplicity of monatomic gas where I got to know that it is proportional to the position space & volume space. $$\Omega \propto V\cdot V_p \;. $$ In order to find the constant of ...
1
vote
1answer
283 views

Why is the derivative of the Fermi-Dirac distribution negative?

Why the derivative of Fermi-Dirac distribution function at absolute zero temperature becomes negative of Dirac_Delta function. The Fermi-Dirac distribution function is \begin{equation} f_{0}(E)=\...
0
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1answer
73 views

Sharpness of multiplicity function

This is quoted from Daniel Schroeder's An introduction to thermal Physics: $$\Omega= \left(\frac{e}{N}\right)^{2N} \; e^{N\ln (q/2)^2} e^{-N(2x/q)^2}\;=\; \Omega_\text{max} \cdot e^{-N(2x/q)^2}\;. ...
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0answers
34 views

Canonical and grand canonical partition function for Hamiltonian H= (N_1-N_2)^2

While preparing for my statistical physics exam I encountered the following problem: A quantum system consisting of two subsystems 1 and 2 is described by the following Hamiltonian: $\hat{H}=c(\hat{...
2
votes
1answer
71 views

Maxwell Boltzmann distribution: Going from momentum to energy

I am learning about the Maxwell Boltzmann distribution, and am trying to convert the equation from momentum into energy, but I'm stuck on changing $d^n p$ into $dE$. I have the equation: $$ E=\frac{|\...
3
votes
3answers
152 views

Physical distinction between mixing and ergodicity

How can one in a very contrasting manner distinguish between the physical meaning of mixing dynamics and that of ergodic dynamics? More precisely, is one a stronger condition than the other? (which ...
6
votes
2answers
341 views

Extending the ergodic theorem to non-equilibrium systems

I try to make this as short and concise as possible. For equilibrium systems in statistical mechanics, we have the Liouville's theorem which says that the volume in phase space is conserved when the ...
2
votes
1answer
97 views

Volume as a choice of measure in phase space

For equilibrium systems, we expect the Liouville theorem to hold. This theorem states that the density function of the states of the system is a constant of motion, which in turn can be translated ...
0
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0answers
42 views

Books on path integral methods [duplicate]

Are there advanced books on applications to physics of the method of path integral? I am aware of some of the standard textbooks on QFT, but looking for more advanced applications of the method.
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0answers
62 views

First law of thermodynamics with additional term

I read in a paper that a "known expression for the heat received by a body" is $$dQ=dU+pdV-\mathbf{v}\cdot d\mathbf{P}$$ where $\mathbf{P}$ is the linear momentum of the body, $p$ is the pressure, $U$...
1
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1answer
47 views

About bosonic, fermionic state in identical particles

The upper picture is my ideas which represent states by using the tensor product. but the lower picture, as you see, includes uppermost states. i don't know how to treat the uppermost states in lower ...
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0answers
63 views

Current status of nonextensive statistical mechanics

A version of the maximum entropy principle is the following. $$\max_{P}~~~ -\sum_i p_i\log p_i$$ subject to all probability distributions $P=\{p_i\}$ satisfying $$\sum_i p_i \epsilon_i = U.$$ ...
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0answers
95 views

How are the real-space RG transformations defined?

I'm reading Shang-keng Ma's book Modern theory of critical phenomena, and I'm a bit confused as to how the real-space RG transformations are defined. Ma basically says that these transformations are ...
2
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1answer
130 views

How to find the normalization constant of Fermi-Dirac distribution function?

The Fermi-Dirac distribution function is given by $$f(E):=\dfrac{A}{{\mathrm e}^{(E-E_{F})\,/\,(k_{B}T)}+1},$$ where A is the normalization constant. When we sum over all the states, we get $1$. ...
0
votes
1answer
83 views

What is a good software for Ideal Gas simulation?

I am looking for a software that simulates the microscopic behavior of an ideal gas, something like this: http://www.youtube.com/watch?v=tEFHkcx2cz0 (unfortunately this program is not openly available)...
1
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1answer
114 views

Quantum mechanics and second law of thermodynamics

Recently I came across this idea of Gibbs that, it is the coarse-grained entropy that always increases, whereas the fine-grained remains a constant. So classically, coarse graining refuses us some ...
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2answers
81 views

Minimization of energy for non-equilibrium systems at steady state (NESS)?

Suppose a non-equilibrium system at steady state. Does the steady state corresponds to the state of some minimal "energy-like", like in classical statistical physics? Example with the Ising model. ...
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1answer
65 views

How to define a non-thermal state? [closed]

I got a very vague question. A thermal state is defined by $$\rho=\frac{e^{(-\beta H)}}{Z_\beta},$$ where $Z$ is the partition function. I want do now calculations with "non-thermal states", but I'...
2
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1answer
53 views

Generallized Canonical Ensemble - Isobaric Ensemble

I am trying to understand the way generalized canonical ensembles like the pressure ensemble are derived from the standard canonical ensemble. In the derivation for the standard form, one defines a ...
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0answers
45 views

Sticky physics of pasta mixture [duplicate]

When you mix cooked noodles or other "prevailing 1D pasta" like spaghetti with other ingredients like olives, pieces of meat (not minced) etc. you will probably experience the fact, that the mixture ...
0
votes
1answer
74 views

How to determine rotational energy of gas molecules

For an arbitrary polyatomic molecular gas, what is the expected behavior of $U_{rot}(T)$, the rotational kinetic energy of the atoms, in the two limits T high and T low? So far, I have written an ...
0
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0answers
98 views

Time between two collisions in a 2D gas

I'm trying to code a simulation of a 2D gas in a box. The molecules are represented by circles of radius $R$ having elastic collisions with the walls only (for now). I read that the average time step ...
0
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1answer
190 views

Can entropy be regarded as energy dispersal?

In several answers here the claim has been made that thermodynamic entropy can be regarded as energy dispersion. See, in particular here, and here and here. This is apparently the pet theory of a ...
2
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1answer
106 views

Monte Carlo with zero-temperature: trapped in a local minimum

I have a problem reaching the correct ground state while performing a Monte Carlo at zero temperature. Some parts of the system get trapped in a local minimum, and for getting the global one (the ...
2
votes
2answers
86 views

how to simulate a steep potential barrier in langevin equation

When simulating a Langevin equation, how is a vertical potential barrier handled? I have the time overdamped evolution of the position $x$, described by $\gamma\frac{dx}{dt}=-V'(x)+\eta(t)$ where $...
1
vote
1answer
59 views

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 ...
3
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0answers
85 views

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 ...
2
votes
1answer
68 views

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 ...
14
votes
7answers
291 views

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 ...
2
votes
1answer
70 views

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 ...
0
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5answers
177 views

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 ...
2
votes
4answers
216 views

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 ...
1
vote
1answer
36 views

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. ...
0
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0answers
15 views

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 ...
0
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1answer
67 views

Speed of spontaneous mixing of different gases

Suppose we have a rectangular box divided into two equal cubic parts by a vertical impenetrable wall. Part 1 of the box contains a standard state mixture of $(1-x)$ mole of gas $A$ (e.g. Oxygen) and $...
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0answers
25 views

conduction band and free electrons the properties of electrons in conduction band

Do electrons in conduction band consider as free electrons? or they are not completely free? so that we can calculate the distribution function and the density if states ??
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0answers
132 views

Change in statistical Entropy negative?

I'm currently stuck with a particular problem: The total energy of a set of molecules in an "isolated" container does not change when the container volume expands by a factor of 2, ...
3
votes
1answer
76 views

Heuristics behind Dirac delta function in Master equation for probability?

I'm reading this paper [Phys. Rev. Lett. 106, 160601 (2011)] and it studies simple diffusion where a particle stochastically resets to its initial position $x_0$ at a constant rate $r$. As you can see,...
5
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2answers
294 views

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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2answers
71 views

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 ...
3
votes
1answer
77 views

Does the canonical partition function count microstates?

The microcanonical partition function is the density of states. The canonical one, from a dimensional point of view, is still a number of states, but does it actually count microstates? I tried ...
2
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0answers
16 views

Role of Chemical potential in Bosonic gas

How does the chemical potential allow us to distinguish different quantum gas, in particular why is it true that for bosonic gas always have chemical potential smaller than or equal to 0.