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

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Partition function of a 3D vibrating string

Is the partition function of a 3D vibrating string a sum of discrete energies, an integral of an energy continuum, or both? $$ Z_{\text{disc}} = \sum_{k=1}^{\infty}g_ke^{-\beta E_k} $$ or $$ ...
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1answer
32 views

Momentum distribution function for a particle in a 1D box

In these notes on statistical thermodynamics (pp. 62), I encountered this [topic: particle in a 1D box]: We shall adopt the initial condition that the probability distribution function has the ...
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0answers
19 views

Find an expression for S(T,x) from tension and specific heat

I'm working on a problem from a Statistical Mechanics lecture series online, and on the homework, I hit a bump in this problem. Here is the problem set, and I'm asking about #1.c. Short version, we ...
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0answers
24 views

Can I measure the volume of a locked room by pumping gas through keyhole and measuring its entropy?

Suppose that I have a locked room and a keyhole in the door and I want to measure the room's volume. Suppose also that I have some "magical" "artificial" inert gas A that doesn't interact with ...
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1answer
31 views

from microscopic to kinetic transport theory

One way to model the dynamics of particles is to find the differential equation of motion of a particle. Of course, this will be nice and easy to do if we have only a few particles (like one-ish, ...
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48 views

Why we need to suppose the chemical potential is zero here?

I've been working on some statistical mechanics problems and one of them asks to compute the pressure with chemical potential zero of a boson gas whose particles do not interact and whose energies are ...
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2answers
45 views

Direct definition of density of states

I've been studying statistical mechanics and in the book there's something the author calls density of states which he introduced in a kind of indirect way. Basically, the author argues that if we ...
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0answers
20 views

What conditions are needed for Onsager reciprocal relations?

I often find a thorough discussion of the conditions that must hold for a theorem lacking, especially in the sense of what they actually mean physically. Could anyone write up what kind of systems ...
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0answers
48 views

Equipartition theorem and virial theorem differences?

The classical virial theorem and the classical equipartition theorem are clearly related. A version of the virial theorem is, \begin{equation} \bigg\langle \sum ^{3N}_{i=1} x_i\frac{\partial ...
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35 views

Time evolution of a classical system

For a harmonic oscillator the Liouville operator is given by $$L = p \partial_q- q \partial_p.$$ Now I have a phase space distribution $f(t,q,p)$ for which it holds (in general) $$f(t+\tau,q,p)= ...
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0answers
39 views

Statistical physics Susskind lecture question? Proof of Boltzmann distribution

In lecture 3 of the following series by Susskind on statistical physics, at 36 minutes in he takes the following step and spends the next 5 minutes discussing it, \begin{equation} f(P_i)=-N\sum ...
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22 views

Mean-field solution of Potts model

The mean-field equation for the three-state Potts model $H= -J∑δσiδσj$ can be derived as follows using this: a) show that $H$ is equivalent to $-J∑Si.Sj$ where, $Si=(1 0) , (-1/2 √3/2 ) , (-1/2 ...
2
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2answers
127 views

Gaussian integral on a Riemannian manifold

How do I estimate the Gaussian integral $\int d^nx \sqrt{g(x)}~e^{-x^2} $ on a Riemannian manifold $(M,g=det~g_{\mu\nu})$? I've tried to consider $\sqrt{g(x)}$ as an analytic function and expanded it. ...
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2answers
106 views

Phase transition without the Peierls' counter argument

Is there any proof of the existence of phase transition in models of statistical mechanics of the Ising type models without using the Peierls' argument and its variations? By models of the Ising ...
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0answers
17 views

Statistical field theories on topological defects

Systems like superconductors and superfluids are often treated by specifying some phenomenological mean field theory where the free energy is given as a functional of some order parameter field. Given ...
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1answer
25 views

steady state and thermodynamic equilibrium

What is the difference between a system being in a steady state and thermodynamic equilibrium ? Can a system be in steady state but not in thermodynamic equilibrium and vice-versa?
2
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1answer
36 views

Fundamental assumption of statistical mechanics

I am confused about the statement of the 'fundamental assumption of statistical mechanics,' as one lecture would put it. For an isolated system in equilibrium, all accessible microstates are equally ...
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1answer
26 views

Partition function is simply temperature if possible sub system energy is continuous?

Partition function is $$Z=\sum_j\exp\left(-\frac{\epsilon_j}{kT}\right)$$ a sum over all possible energy levels $\epsilon_1,\epsilon_2, ..., \epsilon_M$. There must be a finite number of choices ...
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1answer
37 views

What is known about Renyi entropy of a probability density function?

I see most discussions about Renyi entropy to be using either of these two kinds of definitions, for $\alpha > 0, \alpha \neq 1$ $H_{\alpha}(p_i)=\frac{1}{1-\alpha}\log \sum p_i^{\alpha}$ for a ...
2
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0answers
41 views

An integral involving the Bose-Einstein distribution

I'm trying to reproduce the following calculation from the book by Fetter and Walecka (eq. 55.37 and following ones), which represents the temperature dependance of the non-condensate part of a ...
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1answer
40 views

Boltzmann equation collisional operator in thermal equilibrium

Edited after Thomas' answer http://jila.colorado.edu/~ajsh/astr5770_14/grbook.pdf#section.30.5 Question 30.6. "Detailed balance": System is in thermal equilibrium, and the physics of the system is ...
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0answers
25 views

Autocorrelation function corresponding to density of states with significant rotational motion

Most statistical physics textbooks (at least the ones I've found) state simply that the density of states of a system can be found as the temporal Fourier transform of the velocity autocorrelation ...
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1answer
90 views

Total number of photons per unit volume in a box (extremely confusing)

This is a worked example from a text. a) Find an expression for the number of photons per unit volume with energies between $E$ and $E+dE$ in a cavity at temperature $T$. $$n(E)dE = g(E)f(E)dE = ...
2
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1answer
81 views

Does the Unruh effect really describe a thermal bath?

If we consider a free (massless scalar) field $\phi$ in Minkowski space and look at it in Rindler coordinates (which correspond to what an accelerated observer sees), we find that the action of the ...
2
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2answers
41 views

Difference between a reversible change and a reversible process?

Question In thermodynamics what is the difference between a reversible change and a reversible process? Additional information I am new to the topic of thermodynamics and getting confused about ...
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1answer
58 views

Kubo formula for general observables

In the wiki page about Kubo formula, the expectation of some observable under weak time-dependent perturbation is derived. However, from my point of view, some crucial steps are missing. I did the ...
3
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2answers
61 views

Boltzmann distribution for angles?

Consider a system whose sole degree of freedom is an angle $\theta$ that goes from $0$ to $2\pi$. Let $E(\theta)$ be its energy function. Obviously, $E(\theta)$ is $2\pi$-periodic. What's the general ...
3
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123 views

Obtaining the canonical distribution from Fokker-Planck equation?

First I will provide a summary of the problem. Subsequently, I will provide more detail regarding the problem. Please note that entropy is in units of the Boltzmann constant. Summary I have a ...
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0answers
45 views

About the factorial N! in the partition function

After reading these posts: Why is the partition function divided by $(h^{3N} N!)$? , What is the resolution to Gibb's paradox?, and some of these: http://arxiv.org/abs/1012.4111 , ...
2
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1answer
34 views

Einstein model for thermal capacity of solids and indistinguishability of the oscillators

Albert Einstein's theory of thermal capacity of a solids makes the assumption that a crystal is made up from oscillators which of course oscillate, in all three directions. Thus, for N atoms of the ...
5
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1answer
99 views

Why is it difficult to mix helium and nitrogen gases?

I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for ...
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1answer
28 views

Negative absolute pressure with positive absolute temperature

Could I ask if the derivative defining pressure $dU \over dV$ or ${∂S \over ∂V}|_{E,N} $can be negative in processes occuring in system not cosmological but statistical(gases or solids or liquids-I ...
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1answer
54 views

Is there any experimental setup to test if we are Boltzmann brains? [closed]

I am not sure if this subject belongs to mainstream physics. my question is motivated by the fact that I am not sure we could ever test if we are Boltzmann brains. The same happens with string theory, ...
3
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2answers
200 views

Can temperature be a complex number?

Is it possible for a temperature to be a complex number? I want to say "no" but I can't be so sure. If it is possible I would like to know of an example. I found an interesting article which treats ...
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2answers
81 views

How Statistical Physics?

It's a common fact that in physics, we use statistics (or maybe probabilities ) to describe the behaviour of a system. It was from the statistical analysis of a system where quantum statistics arose ...
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1answer
52 views

How can we be sure the Maxwell speed distribution equation is always a rational number?

The Maxwell speed distribution equation is given as $$f(v) = 4\pi \biggl(\frac{m}{2\pi kT}\biggr)^{3/2}\exp\biggl(-\frac{mv^2}{2kT}\biggr)v^2.$$ The left hand side gives the fraction of molecules ...
2
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1answer
57 views

Understanding chemical potential in AdS/CFT

I always find it very difficult to understand the notion of chemical potential physically/intuitively unlike pressure and temperature in statistical mechanics. Can some one suggest some nice ...
2
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0answers
38 views

Local and global detailed balance

I'm taking a course on nonequilibrium statistical mechanics and I encountered the terms local and global detailed balance. I'm a bit confused about what is their exact definition and what is the ...
0
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1answer
23 views

Bending moment and Shear force

Do bending moment and shear force of a beam depend on it's cross sectional dimentions?? Since all the diagrams which I have draw so far don't involve any cross section details. So I think they do not ...
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0answers
26 views

One question about critical exponents for first order transition free energy [closed]

I've got a problem to calculate critical exponents for theory given by Landau free action: $$ \tag 1 L = L_{0} - \frac{1}{2}(\nabla m)^{2} + atm^{2} + dm^{3} + bm^{4} - hm, $$ where $$ -\infty < ...
0
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2answers
57 views

Definition of an irreversible process

I'm a little bit confused as to why quasi-static process cannot lose energy to friction in order to be reversible. This is how I'm thinking: Suppose you have a container of gas with a piston, and on ...
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0answers
32 views

Non-trivial integral with the Bose-Einstein distribution and Cosine function

When I consider the Casimir interaction between an atom and a perfect conducting slab I find the following non-trivial integral: $$\int\limits_0^\infty {\frac{{\cos \left( mx \right)}}{{x + ...
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1answer
74 views

Is 'Boltzon' an accepted name for particles following Maxwell-Boltzmann (MB) statistics?

In my curriculum during one of my statistical mechanics visiting lecture classes, our teacher was referring comparatively macro particles following MB statistics as "Boltzon". But I have searched ...
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0answers
58 views

In the derivation of canonical distribution why does one linearize entropy (and not something else?)

I know that there are (at least) two ways to derive the canonical distribution. I am interested in the one where one considers the entropy of the reservoir (with which the system we are considering ...
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0answers
24 views

What is normal fluctuation?

I was reading Statistical Mechanics (second edition) by Kerson Huang. On page 146, after equation 7.14, there is a reference to normal fluctuation. What is it? Here is the relevant part from the ...
0
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0answers
29 views

Problem in deriving the second term in perturbation expansion the quantum ising model

So I'm trying to derive the perturbation expansion for one particle states in the quantum ising model (Sachdev 2011 QPTs which this is derived from ) $$ H_I= - J g \sum_i \sigma_i^x - J ...
2
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1answer
62 views

Boltzmann equation in cosmology

I have a question about the Boltzmann equation in cosmology. Im trying to understand how this can hold? Where does the logarithmic terms come from? It is explained quite well here ...
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1answer
140 views

Difference in partition function of classical and quantum Ideal gas

First, I have read this question:What is meant by the term "single particle state" There is an analysis going on in my book (Mandle F. Statistical Physics) that has brought me in a ...
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0answers
27 views

Work done by a gas in an expansion [duplicate]

1) Consider a gas expanding quasistatically and reversibly from $V_1$ to $V_2$ at constant temperature. I want to calculate the work done. So by convention work done by a system is a negative quantity ...
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1answer
42 views

Struggling with whether its $\pm p dV $

I am struggling to understand when calculating the work done by a gas whether it is postive or negative p. It my notes and in many other notes sometimes it is $-pdV$ and sometimes it is $pdV$. I ...