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

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Can the second law of thermodynamics be violated in a small enough system if tried repeatedly enough?

Second law of thermodynamics is observed in the universe because statistics favors it, right? And in large enough system this statistical tendency becomes certainty. Does it also mean that negative ...
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41 views

Intuition on Gibbs measures

I am (roughly) aware of the way Gibbs measures are used to solve physical systems (e.g. the Ising model). We can basically boil it down to pinpointing a Hamiltonian. My question is, consider a ...
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32 views

Statistical mechanics - average particle energy, average kinetic energy

I'm looking at derivations for average particle energy giving $E=kT$: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/bolapp.html And average particle kinetic energy giving $K_E=\dfrac{3}{2}kT$: ...
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47 views

Deriving the correlation function of a system interacting with a bath of harmonic oscillators

I'm working on the book Quantum Effects in Biology by Mohesni et all. My question is however not biology related, it is about a section on quantum master equations in the weak system-bath coupling ...
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94 views

How to derive equation for time it takes photons to diffuse through the Sun

I am wanting to use the Rosseland radiative heat flux equation to find the time it takes for photons to diffuse through the sun. The answer I am wanting to derive is: $$\tau_D~\frac{\rho \bar C_p R^...
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31 views

What is melting / boiling from the statistical viewpoint?

Microscopically, solids are usually described as "completely ordered" and "strongly bound", liquids "somewhat ordered", and gases "unbound" and "disordered". Thermodynamics predicts that the ...
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35 views

probability of striking the circular ring by gas molecules

In kinetic theory we use probabilistic case to derive pressure, no. Of molecules having speed c to c+dc or in such cases.and to derive such equations we introduce a term called "SOLID ANGLE" I come ...
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31 views

Confusion about the number of micro states and approximating it for large number of particles

Hopefully after reading the meta site, I can now rephrase the question as more relevant to this site, this is a question related to statistical physics: Let us suppose we are given a system with $...
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37 views

Ising model as quantum model?

I've read in a few papers things that use the fact that the $2D$ Ising model can be interpreted as a $1+1$ quantum spin model. I haven't been able to find this description and would like to read about ...
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13 views

Numerically extracting free energy in renormalization procedure

I have some doubts about how to apply real space renormalization numerically. I understand the theoretical concept, and how we require $Z'=Z$, being $Z'$ the partition function of the renormalized ...
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27 views

Magnetisation of a degenerate electron gas in a weak field?

So I am looking at Landau's and Lifshitz's "Statistical Physics, Part I" chapter on degenerate fermi gases and specifically at chapter on Pauli's Mangetism or magnetism of degenerate electron gases, §...
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24 views

Perodic boundary conditions vs Dirichlet?

I have been working through several examples recently involving particles in boxes (when finding the partition function of an ideal gas for example or looking at photon gases). I have seen two ...
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49 views

Entropy of fermi gas at $T=0$

Does the entropy of ideal fermi gas go to zero , in accordance with third law of thermodynamics? Consider a system of three fermions in a 3D box. The first fermion goes to the ground state of the ...
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44 views

Is the formula of temperature $ \frac{1}{T}= \left(\frac{\partial S}{\partial U}\right)_{V,N}$ applicable to all type of ensembles?

I have seen multiple posts on this page that explained the statistical definition of Temperature as the derivative of the Entropy to the energy: \begin{equation} \frac{1}{T}\equiv \left(\frac{\...
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51 views

The Ideal Gas Equation in higher dimensions

Basically I wanted to know whether or not the ideal gas equation, $PV=NkT$ would hold in higher dimensions? If so, how would you go about proving this? I can't see any reason as to why it shouldn't ...
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27 views

Forward and backward work distributions in fluctuation theorem

Fluctuation theorems such as Jarzynski equality and Crooks theorem (Link), show that $\frac{P_f(W)}{P_b(-W)}=\,exp[\beta(W- \,\Delta F)]$ where $W$ is work done on the system during each ...
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53 views

Books on Introductory Statistical Mechanics

Can anyone recommend a good book on Basic Statistical Mechanics? I have an engineering background and had to go through loads of different books to learn General Relativity. I found Peter Collier's A ...
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39 views

Does it take the same amount of time, it takes for a system to get to a low-entropy (fluctuation) state from equilibrium, to go in the other way?

Let a system be in a state of fluctuation - a state of low-entropy at $t_0\;.$ Then before and after a sufficiently large but finite time-interval, the system would again be at equilibrium. As the ...
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23 views

Radiation collapse to black hole

I want to find the temperature at which radiation in AdS will collapse to form a black hole. I have even found a reference that gives the answer but I cannot understand it: http://srv2.fis.puc.cl/~...
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82 views

Mathematical definition of reversible processes

If I label an initial thermodynamic state as $\psi$ and the final thermodynamic state as $\xi$ then can I say that under a reversible process the two states are related to each other by a continuous ...
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77 views

Good thermodynamics/statistical mechanics books that treat the apparent paradoxes in the theory

I am working on a small project mainly concerning the Gibbs and mixing paradoxes arising in thermodynamics/statistical mechanics. Still cannot find good literature on the topic. Any suggestions (I ...
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29 views

Spin interaction of Virtual Phonon's forming Cooper Pairs

Im confused about the spin of virtual Phonons, my lecture notes suggested that even spin bosons repel opposite charges, and it also suggested that cooper pairs form by considering the "Charge" to be ...
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48 views

annealed randomness vs quenched randomness

what is meaning of annealed randomness and quenched randomness? in this article used this phrase to compare the model and earthquake data.
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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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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{...
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60 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, $U$...
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62 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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56 views

Proof of periodicity of Floquet Green's function

It is claimed in many papers that the two-time Green's function in time periodic Hamiltonian case is periodic in the average time, i.e. \begin{equation} G(t+T,t'+T)=G(t,t') \end{equation} when $H(t+...
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30 views

Phase-space average equal to the quantum mechanical average in the early universe

I was reading Mukhanov's book of cosmology http://www.amazon.com/Physical-Foundations-Cosmology-Viatcheslav-Mukhanov/dp/0521563984 , specifically about symmetry restoration in the early universe ...
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113 views

Ising model at high vs. low temperature

The output of the Ising model over a 2D binary lattice looks to have spin states uniformly distributed over the lattice for high values of the temperature parameter with the output attaining ...
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27 views

Partition Function And Macroscopic Properties

In renormalization group transformations, partition function is fixed. My question is which thermodynamic properties are fixed in a renormalization group transformation.
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Canonical treatment of thermalization of two gases at different temperatures

I'd like to understand the thermalization process when two gases of different species and different temperatures are allowed to mix in an insulated container, interacting only through an elastic ...
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458 views

What is the physical meaning of a Partition Function in Statistical physics?

In many places in statistical physics we assume the partition function. To me the explanations after partition functions are most of the times clear but always wonder why a partition function and what ...
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51 views

What is the relation between scattering amplitudes, fluctuations, response functions and correlations in macroscopic equilibrium systems?

In Kardar's book Statistical Physics of Fields, he mentions that that correlations at different length scales can be measured by scattering. If its electric correlations, you would scatter light and ...
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61 views

Is there a local canonical ensemble partition function for a Bose-Einstein gas?

The grand canonical partition function for a Bose-Einstein gas is $$ Z_{\text{grand bos}} = \exp \left( \sum_{j=0}^{\infty} -\ln \left( 1-e^{\beta(\mu-\epsilon_j)} \right)g_j \right) $$ where $\beta$ ...
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42 views

A functional average calculation confusion within Gaussian planar model's RG

I am trying to follow some detailed calculation in a famous paper [John, B. Kogut, Rev. Mod. Phys. 51, 659 (1979), An introduction to lattice gauge theory and spin systems]. More precisely, please ...
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41 views

Making Pudding; A complicated non-equilibrium statistical process?

There are a lot of non-equilibrium processes examples given in physics literature. But some processes that are present in everyday life are not treated. As an example, the formation of pudding can be ...
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37 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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70 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 _iP_i\...
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84 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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41 views

Thermal Equilibrium of two thin sheets

While reading Gibbs' Elementary Principles in Statistical Mechanics I came across this footnote: The most simple test of the equality of temperature of two bodies is that they remain in ...
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177 views

Quantum Monte Carlo for harmonic oscillator

I'm trying to calculate harmonic oscillator using quantum monte carlo (path integral and metropolis algorithm). It's one particle in harmonic potential. I know the theory. One divides the partition ...
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111 views

How to derive entropy transport equation from heat equation?

Suppose I have heat equation: $$ \rho (\partial_{t} + (u \cdot \nabla)) T = -\nabla \cdot \mathbf R, $$ where $\mathbf R$ - some vector and $T$ - temperature. How to get the equation for entropy $S$ ...
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167 views

How is partition function related to ordinary generating function?

Ordinary generating function can be used to solve combinatorial enumeration problems. Now if the energy levels are discrete, say $g_i$, and if one want to count how many ways one can add up $g_i$ ...
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70 views

Proving the Virial theorem

Consider the expectation in the canonical ensemble defined by $$\left\langle x_i\frac{\partial \mathcal{H}}{\partial x_j} \right\rangle=\frac{1}{Z}\int d\Gamma x_i\frac{\partial \mathcal{H}}{\...
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136 views

Construction of free energy based on Landau theory

Consider an Ising model system where the total energy is $E = −J \sum_{<ij>} S_iS_j $, $S_i = \pm 1$ and $< ij >$ implies sum over nearest neighbours. For $J < 0$ the ground state of ...
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65 views

Time evolution of the density of phase points for an ensemble

I want to calculate the time evolution of the density of phase points for an ensemble of N harmonic oscillators. However, I intended to do so without using the Liouville equation. Sure, I want to ...
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61 views

Debye-Huekel Theory and the continuum approximation

This question stems from a problem I was doing on the Debye-Hueckel theory. It says that the continuum approximation which underlies the Debye-Hueckel theory is valid provided that $\lambda_D \gg r_{...
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72 views

grand-canonical ensemble

I was wondering if the following reasoning is correct for example for electrons in the classical or qm grand-canonical ensemble? Is it always valid in the grandcanonical ensemble to calculate the ...
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83 views

How to apply Wick's theorem in 2nd quantization for Spin Density Operators?

I am trying to work out a correlation function consisting of two spin density operators. Once I rewrite everything in 2nd quantized form, I am unsure of how to apply wicks theorem because the paul ...