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

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59 views

Chemical potential of photons [duplicate]

Why do photons have zero chemical potential and what is its the physical significance? From what I know the chemical potential could be interpreted as the energy per unit particle that is put into a ...
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2answers
97 views

Free electron gas in two dimensions

Can someone give a qualitative description on why the density of states for a two dimensional free electron gas is independent of energy while it is not in one and three dimensions? In one dimension ...
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1answer
28 views

Probability distribution of two particle types system

Suppose that particles of two different species, A and B, can be chosen with probability $p_A$ and $p_B$, respectively. What would be the probability (and distribution) $p(N_A;N)$ that $N_A$ out of ...
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1answer
79 views

Statistical count

I am reading the book"Heat and Thermodynamics" by Mark Waldo Zemansky and Richard Dittman. In the chapter "Statistical Mechanics" it says if I have $N_{i}$ distinguishable particles in any of $g_{i}$ ...
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1answer
94 views

Is there a known equation for evolution of classical particle probability density?

Suppose we have some very imprecise knowledge of classical particle's coordinates and momentum: what we can only tell is the probability density to find it in some point of phase space. This is ...
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54 views

Is it possible to define a notion of temperature in a microcanonical ensemble?

I am thinking of a mircrocanonical ensemble as a finite system for which the number of particles, volume and the total energy is fixed. Is there a more refined view of this? Can I think of ...
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64 views

What real experimental systems are well-described by Glauber-Ising spins?

I'm hoping for references to actual physical systems in which all or at least most of the following can be simultaneously characterized: the spin flip rate, the temperature, and a relaxation or ...
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1answer
184 views

RMS Free Path vs Mean Free Path

I am trying to determine the mathematical difference between mean free path and root-mean-square free path. For an ideal gas, the relaxation time is $$\tau=\frac{1}{\sqrt2 \pi nd^2 \bar v}$$ and the ...
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98 views

Statistical mechanics of a coin toss

I'd like to ask some questions about flipping two coins related to statistical mechanics, e.g. microcanonical distribution, phase space distribution function etc... after I rephrase the coin flipping ...
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130 views

phase-space volumes or cells for N particle system

For N non interacting spinless particles in a volume, we have 3N degrees of freedom and we can divide the phase space into 6N dimensional cells of volume h raised to power 3N. And each cell ...
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1answer
115 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 ...
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1answer
111 views

Quantum Fourier Transform and Entropy

QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of ...
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1answer
73 views

Three-body correlation function in kinetic theory

In Kinetic Theory, one studies the evolution of a system of $N$ particles interacting with each other. We use the notation $\boldsymbol{w}_{i}$ to describe the coordinates in phase-space of each ...
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2answers
85 views

Statistical Mechanics - Distribution of Energies

Consider a state space $\mathbb{X}$. The probability density function under a canonical ensemble is given by the Boltzmann distribution $$\pi_{\mathbb{X}}(x)=\frac{e^{-\beta ...
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2answers
208 views

Connection between QFT and statistical physics of phase transitions

I have heard that there is a deep connection between QFT (emphasized by its path-integral formulation) and statistical physics of critical systems and phase transitions. I have only a basic course in ...
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2answers
47 views

Is there an analogue to the role of vapor in liquids and gases, but for solids and liquids?

It seems common for an ordered phase to have some amount of disorder present. For example, the average moment of a ferromagnet is less than maximum except at T=0 due to the presence of fluctuations. ...
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105 views

Boltzmann distribution: derivation from canonical distribution

I'm trying to understand the Maxwell-Boltzman Distribution, and in particular the derivation from the boltzman distribution for energy. I have successfully created an incorrect derivation, but I'm not ...
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1answer
81 views

A real gas with gravitation-like interaction

Consider a system (a gas) of point-like particles with a gravitation-like interaction (potential) $V(r) \sim \frac{1}{r}$ between pairs of them. One can rule out statistically that two particles will ...
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1answer
41 views

Can electrons coincidentally flow along a circuit to cause current?

My understanding of circuits which are not supplied an e.m.f. is that the electrons randomly just flow about in random directions, and since there's so many of them, probability dictates that any ...
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5answers
133 views

How can point-like particles in an ideal gas reach thermodynamical equilibrium?

Having learned that the particles of an ideal gas must be point-like (for the gas to be ideal) I wonder how they can reach thermodynamical equilibrium (by "partially" exchanging momentum and energy). ...
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22 views

What is Fermi energy and Fermi level? [duplicate]

What is meant by Fermi level and Fermi energy? And what is the difference between the two?
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2answers
110 views

How are degrees of freedom and energy related in classical theory?

How are degrees of freedom and energy related in classical theory? How do we come to know that each quadratic degree of freedom classically contributes a factor of $\frac{k_{B}T}{2}$.
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1answer
151 views

Which transformations are canonical?

Which transformations are canonical? Why do canonical transformations preserve the measure of integration in phase space?
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2answers
248 views

Nonequilibrium thermodynamics in a Boltzmann picture

The Boltzman approach to statistical mechanics explains the fact that systems equilibriate by the idea that the equillibrium macrostate is associated with an overwhelming number of microstates, so ...
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57 views

What is conductivity?

I read that if we have spin $\frac{1}{2}$-particle, where a magetic force acts on, then the force is given by a drift speed times a conductivity. This conductivity is determined to be $\frac{kT}{D}$, ...
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1answer
70 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 ...
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3answers
655 views

Why must the particles of an ideal gas be point-like?

Why is a gas of elastically colliding hard balls of finite size not ideal? Respectively: Why is it essential that the particles of an ideal gas are point-like? Especially: Which ...
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2answers
107 views

System in mechanical but not thermal equilibrium

Let's say there are two systems which can interact by a moving wall but cannot exchange heat. Then the system will be in mechanical, but not necessarily in thermal equilibrium. The maximality of ...
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1answer
52 views

Relation between solutions to Yang-Baxter equations, integrability and exact solvability?

Wikipedia mentions that there is an implication: Yang-Baxter solutions yield integrable models, what 1D systems concerns. In arbitrary dimensions, what is the relation, if any, between solutions to ...
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274 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 ...
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78 views

Fugacity of the fermi gas

It can be shown that in the high temperature exploration of the Fermi gas, the Fermi function may be expanded to second order in $e^{\beta \mu}$, where $\beta = 1/kT$ and $\mu$ is the chemical ...
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95 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 ...
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2answers
132 views

How to deal with mean field method in antiferromagnetism?

There are lots of ways to apply the mean field method to deal with the Ising model whose ground state is a ferromagnetic state. Hence, it is easy to find the order parameter named magnetization to ...
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27 views

Can the short-time dynamics of an open quantum system be approximately unitary?

Considering the physics of an open quantum system described by a Hamiltonian $H=H_S+H_E+H_{SE}$, where the subscript $S$ refers to the system of interest, $E$ to the environment and $SE$ to the ...
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2answers
412 views

Physical significance of negative temperature

I read some answers regarding negative temperatures but I think my question is new. I want to know that what is the physical significance of negative temperature. Suppose I say a body has ...
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1answer
71 views

Failure of a simple stat mech simulation

so I did a simple simulation that I thought would yield a Boltzmann distribution, but it failed to, and I was wondering if anyone has insight into why it failed. Ok, so I had a simple discrete system ...
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129 views

The Maxwell and the Boltzmann distributions

I am trying to understand where the Boltzmann distribution comes from. I recently learned some interesting things of which my interpretation follows below. Did I interpret correctly? If so, is this ...
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1answer
204 views

Understanding collision terms in Boltzmann equation

I am reading a paper that deals with the Boltzmann equation. They add a collision which is supposed to account for collisions which happen when particles are within a radius of $d$ from each other. ...
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1answer
83 views

Pathria's “Statistical Mechanics” first edition [closed]

Does anyone know where I could find and purchase the book "Statistical Mechanics" by R. Pathria, in 1st edition (the 2nd and the 3rd are readily available, but I really need the first). I believe the ...
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82 views

Occupation probability in grand canonical ensemble

I have a system with energy spectrum which has two groups of $N$ degenerate levels (the gap between them is $E$). There are $N$ non-interacting fermions in the system. What is the occupation factor at ...
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1answer
76 views

Microcanonical Ensemble

I'm having difficulty understanding a statistical mechanics problem. I'm missing some basic understanding of counting the minimum energy states. My thought is that there are three states to choose ...
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1answer
142 views

What is the resolution to Gibb's paradox?

This question is essentially a duplicate of Gibbs Paradox - why should the change in entropy be zero?. The question concerns the following situation: I have some gas of identical particles and they ...
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62 views

Statistical Mechanics: Most probable orientation of grain particle in gas chamber?

I'm in an introductory statistical mechanics course, and we've been posed the following situation: Long-shaped dust particle (so imagine something like a grain of rice) is placed in a gas chamber (so ...
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495 views

Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} ...
2
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1answer
82 views

Experimental Evidence of Random Tiling Limit Shapes

In the area of random tilings, there are many results that fall under the term "Arctic Circle Theorems." This roughly means that if one chooses a tiling of a specific region uniformly at random, then ...
3
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1answer
356 views

Fermi-Dirac distribution derivation?

I am trying to derive the Fermi-Dirac statistics using density matrix formalism. I know that $$<A>= Tr \rho A.$$ So I started from $$<n(\epsilon_i)>= Tr \rho n(\epsilon_i)=\frac {1}{Z} ...
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1answer
99 views

QHO in Microcanonical Ensemble: Problem with alternate derivation

I am working through Franz Schwabl's book on Statistical Mechanics, and he has a number of derivations of thermodynamic quantities that are different than those I have seen before. I am also having ...
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1answer
77 views

How do we know that the Virial Expansion exists?

How do we know that the Virial Expansion exists? How do we know that we may always write $\frac{p}{kT}$ as a power series in $\frac{N}{V}$? That is, how do we know that there exists $B_{i}$ so that ...
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3answers
160 views

How to calculate critical temperature of the Ising model?

Can someone name a paper or book which calculates the critical temperature of the Ising model from scratch? It might be a book and should contain the necessary prerequisites. I have had a basic course ...
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1answer
75 views

Why is $B(T)\approx b(T-T_C)$ near critical point $T_C$ in Landau theory?

In Peskin&Schroeder page $270$ equation $(8.4)$ you see that they approximate the function $B(T)$ near the Curie temperature as $$B(T)\approx b(T-T_C)$$ i.e. they omit $B(T_C)$ in the Taylor ...