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

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7
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3answers
85 views

What would be non-ergodic physics processes?

As the title says, what would be non-ergodic processes that occur in statistical physics? Many textbooks do not really cover ergodicity really well so I ask this question. I can't suddenly remember ...
1
vote
3answers
197 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
4
votes
2answers
155 views

Why is the Gibbs Free Energy $F-HM$?

With magnetism, the Gibbs Free Energy is $F-HM$, where $F$ is the Helmholtz Free Energy, $H$ is the auxiliary magnetic field, and $M$ is magnetization. Why is this? Normally, in thermodynamics, we ...
2
votes
2answers
57 views

Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
1
vote
2answers
265 views

Fermi-Dirac Statistics

In Fermi-Dirac statistics the probability of being in a certain energy state is $$f(E) = \left[1 + \exp\left(\frac{E-E_F}{k T}\right)\right]^{-1}$$ In the area that I'm looking at the texts always ...
1
vote
2answers
213 views

Calculating the change in entropy in a melting process

I have a homework question that I'm completely stumped on and need help solving it. I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
0
votes
2answers
107 views

What are correlated magnetic moments?

My book has the following sentence and I don't understand what correlation or lack of correlation means: At high temperature the magnetic moments of adjacent atoms are uncorrelated (to maximize ...
14
votes
1answer
141 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each ...
13
votes
1answer
273 views

How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...
5
votes
1answer
39 views

Minimum connectivity required for mean field to be a good approximation?

In spin models, it is known that mean field becomes a better approximation as the connectivity increases. My question is: Is there an estimate for the threshold connectivity (as a function of the ...
4
votes
1answer
143 views

Semi-conductors

Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states. I'd like to know why the mean number of excited electrons takes the form $$\bar n={N\over ...
4
votes
1answer
325 views

Renormalization Group and Ising with d=1 and D=1

I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations $K'(K)$, $q(K')$ $K(K')$, $q(K)$ between the coupling costants. My problem arise ...
4
votes
1answer
390 views

upper critical dimension in field theory

Is there field theory which describe a second order phase transition without upper critical dimension ? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.
4
votes
1answer
927 views

Infinite-range 1D Ising model + Hubbard-Stratonovich-Transformation

I have a probably quite simple question RE the HST. After some work, I obtain as the partition function for the infinite range 1D Ising model $$Z = \int_{-\infty}^\infty \frac{dy}{\sqrt{2\pi / ...
3
votes
1answer
73 views

Cluster Expansion vs Cluster Decomposition

Are the cluster expansion (which we encounter in Statistical Physics), and cluster decomposition (in Quantum Field Theory) related to each other? (I have a reason to believe they are)
3
votes
1answer
42 views

What is an intuitive explantion for the fact that the Maxwell-Boltzmann distribution of energies is independent of mass?

If you take the Maxwell-Boltzmann distribution of velocities (which depends on the mass) and substitute $v=\sqrt{\frac{2E}{m}}$ you get the distribution for the energies, which turns out to be ...
3
votes
1answer
52 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
3
votes
1answer
270 views

Are black hole states completely mixed?

A completely mixed state is a statistical mixture with no interference terms, and (QMD, McMahon, pg 229): $$\rho = \dfrac{1}{n}I$$ $$Tr(\rho^2) = \dfrac{1}{n}$$ Are black hole quantum states ...
2
votes
1answer
36 views

Numerical Ising Model: Swendsen–Wang algorithm, Percolationtheory?

When you look at the original paper of Swendsen and Wang in 1987: "Nonuniversal critical dynamics in Monte Carlo simulations" it is somewhat mentioned that the proposed algorithm uses percolation ...
2
votes
1answer
94 views

Thermodynamics, chaperones : How to model polymer fragmentation

Living polymers are well described by equilibrium statistical physics. Now I would like to consider a case were living polymers undergo fragmentation due to chaperones. I can think of a kinetic ...
2
votes
1answer
85 views

Lennard-Jones induced pseudo-molecules

It can be shown that the Lennard-Jones potential - which describes the interaction between particles in non-ideal gases - gives rise to pseudo-molecules: after a triple "collision" of three ...
2
votes
1answer
125 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
1
vote
1answer
39 views

How can the microstates be measured with zero energy expenditure?

James P. Sethna. Statistical Mechanics. Exercise 5.2: What prevents a Maxwellian demon from using an atom in an unknown state to extract work? The demon must first measure which side of the ...
1
vote
1answer
105 views

What is the probability of ice in boiling water?

Ice crystals are spatially ordered, and in every randomness there is a low possibility of temporarily order. If given enough boiling water, and sufficient time, could local clusters water molecules ...
1
vote
1answer
94 views

2nd order phase transition trouble deriving coefficient in fluctuations analysis

I can't get one of the coefficients in the equation for $T < T_c$ in the bottom, specifically the equation with the factor of two. any help appreciated. Consider an ising type expansion of the ...
1
vote
1answer
160 views

Bose–Einstein statistics exercise

I've a basic Bose–Einstein statistics exercise. I've tried to solve it in two ways, but each way gives a different result. We have $n$ identical bosons without interactions at temperature $T$. There ...
0
votes
1answer
38 views

Statistical Mech Problem

i need to derive a formula for the photon gas correlation function $\left\langle\partial n_i\partial n_j\right\rangle $ where $\partial n_i=n_i -\left \langle n_i \right \rangle$ whilst solving i ...
0
votes
1answer
110 views

General way to model baths? Harmonic Oscillators valid?

I am trying to model an open system interaction without making strong assumptions on coupling strength or temperature. In general i understand that open systems are modeled by a Lindbladian, but as ...
0
votes
1answer
148 views

Virial Theorem and the Energy in a Gas

I clearly am interpreting the Virial Theorem incorrectly, but I don't know how. In dipole gases, the molecules can exhibit five kinetic modes, while they can only experience 2 potential modes. Doesn't ...
-1
votes
1answer
857 views

Partition function for a microcanonical ensemble

Is it possible to write down a partition function for a microcanonical ensemble?
0
votes
0answers
68 views

Why is the transition into N proportional to N+1?

I am having trouble understanding the origin of the bosonic stimulated emission. How can I qualitatively understand why bosons Boson's attract each other into similar quantum states. The furtherst I ...
0
votes
0answers
67 views

Edwards-Anderson Hamiltonian of a Hopf link

I was calculating the Edwards-Anderson Hamiltonian of a Hopf link. A hopf link is like attachment 1. I have drawn the Seifert surface of that link. The surface is shown in attachment 2. It also ...