# Questions tagged [statistical-mechanics]

The study of large, complicated systems by means of statistics and probability theory, in order to extract average properties and to provide a connection between mechanics and thermodynamics.

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### The cavity method of Ising model in infinity dimension and dynamical mean field

In the article "Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions" chapter III.A, when discussing the cavity method of Ising model, the ...
1 vote
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### Regarding calculation the moments of a random variable whose probability distribution obeys the Fokker Planck equation

I was going through Van Kampen's Stochastic Processes in Physics and Chemistry, and I was trying to solve the exercises from Chapter 8 about the Fokker Planck equation (just in case context could help ...
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### What are critical dimensions in statistical field theories (SFTs) and quantum field theories (QFTs) and how do they relate to divergences?

My question is the following. Statistical field theories (SFTs) and quantum field theories (QFTs) are usually associated with some upper critical dimension (UCD) and lower critical dimension (LCD). ...
58 views

### Metropolis-Hastings and underlying Markov process

I tried to understand the workings of the Metropolis-Hasting algorithm. As far as I can understand, it allows to draw samples from an unknown distribution $T(x)$ as long as a function proportional to ...
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1 vote
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### Boltzmann vs Gibbs definition of entropy [duplicate]

I am learning Statistical Mechanics and I have a question regarding different definitions of (statistical) entropy. If we use Boltzmann's definition: $$\sigma \propto\ln(W)$$ Where $\sigma$ is the ...
1 vote
263 views

### Currently self-studying QFT and The Standard Model by Schwartz and I'm stuck at equation 1.5 in Part 1 regarding black-body radiation

So basically the equation is basically a derivation of Planck's radiation law and I can't somehow find any resources as to how he derived it by adding a derivative inside. Planck says that each mode ...
1 vote
35 views

### Proving a relationship involving the chemical potential [closed]

I need to prove the relation $$\left(\frac{\partial \mu}{\partial N}\right)_{T,V}> \left(\frac{\partial \mu}{\partial N}\right)_{T,P}.$$ One may start with the total differential of the internal ...
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### Pure state vs mixed state in this example

Consider, I have a quantum state $|\Psi\rangle$, such that : $$|\Psi\rangle=c_1|\psi_1\rangle+c_2|\psi_2\rangle$$ This is defined as a pure state, since I have complete information about the system. ...
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### Are photons with different frequency distinguishable?

When i learn statistical mechanic, the teacher told me that photons with different frequency are distinguishable, i confused. And the teacher say also photons with different polarization, direction ...
25 views

### Are all Local Observables Measured on Gibbs States Analytic as a Function of Temperature Away from Phase Transitions?

Let $\rho(\beta)=e^{-\beta H}/Z$ be the Gibbs state of a quantum Hamiltonian, and $H$ is some local Hamiltonian on $N$ particles, and $Z(\beta)$ is its partition function. Suppose I measure some local ...
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36 views

### The microcanonical ensemble surface distribution function

on page 58 of the book "the principles of statistical mechanics" by Richard C. Tolman, there refers to a formula for the surface density of distribution in microcanonical ensemble, which is: ...
### If temperature is the expected value of kinetic energy: $T\propto \text{E[}E_k\text{]}$, what is exactly entropy in statistical similar terms?
If temperature is the expected value of kinetic energy: $T\propto \text{E[}E_k\text{]}$, what is exactly entropy in terms of moments similar to expected value? Is there a relation with moments and ...