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

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263 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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664 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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77 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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1k 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} -\frac{\hbar^{2}}...
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1answer
147 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 ...
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1answer
1k 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
176 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
126 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
446 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
86 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 ...
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110 views

Law of equipartition

Law of equipartition predicts the heat capacity of gases correctly. It assumes that inter-molecular attraction in gases is negligible (which is true). But for solids, inter-molecular attraction is not ...
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5answers
2k views

Does it take infinite energy to create a perfect vacuum?

Question is inspired by a recent burst of perpetuum mobile-type questions. It would be nice if one could simply discard them all (or at least the huge class that assumes some kind of perfect vacuum to ...
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106 views

Langevin equation

A molecule consists of two atoms whose centers are located at $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The atoms are connected by a bond that can be approximated by a harmonic spring, so that ...
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2answers
113 views

Temperature limit on entropy of a paramagnet

We have $$S=Nk_B[\ln(2 \cosh(x)) - x \tanh(x)]$$ where $$x = \frac{\mu B}{k_BT}$$ In need to show that at low temperatures entropy $$S \approx Nk_B2xe^{-2x}$$ I wrote out the $\cosh(x)$ in terms of $...
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3answers
3k views

What is the meaning of Boltzmann definition of Entropy?

I would like to ask if someone knows the physical meaning of Boltzmann's definition of entropy. of course the formula is pretty straightforward $$S=K_b\ln(Ω)$$ but what in the heck is the natural ...
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1answer
129 views

Entropy and probability

I read "The NEW world of Mr. Tompkins" and I'm not sure with one of the Gamow's equation. When he calculated the probability of entropy, he used this reasoning: "How likely is a situation that all the ...
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2answers
226 views

On the distinction of past and future: could one theoretically reverse direction of particles and cause time to appear to go backwards?

Based on my understanding of physics after seeing The Distinction of Past and Future on Project Tuva, there is no distinction between past and future on a fundamental level- all particle interactions ...
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1answer
279 views

About the gauge formalism in statistical quantum field theory

I would like to understand a bit more the aspects of the gauge theory in statistical field theory. In particular, I would like to understand how the replacement $\tau \rightarrow it/\hbar$ is ...
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5answers
2k views

Is the $N$ factorial in the Partition function for $N$ indistinguishable particle an approximation?

I suspect that the $N$ factorial in the partition function for N indistinguishable particles $$ Z = \frac{ Z_0^N } {N!} $$ is an approximation. Please someone correct me if I am wrong and why or why ...
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1answer
85 views

Equivalence between gibbs states representations with different temperatures

I'm asked to answer this question: why two Gibbs states with different temperatures give the same (GNS) representation? Actually, I can't even imagine if this is true and if not how to find a counter ...
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1answer
145 views

How does the Lennard Jones Potential changes for interaction between particles of different sizes?

I am interested in incorporating a Lennard-Jones potential in a simulation. When the interaction only involves the same type of particle, with same characteristics, we can use reduced units, scaling ...
2
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1answer
98 views

Details in the derivation of the second law starting from the phase space volume

I had a question on one of the details of the derivation of the second law of thermodynamics starting from the phase space volume. I'll type out what I understand so far: Letting the Hamiltonian ...
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2answers
78 views

Entropy of a chain

A chain has N segments which can be oriented in either the x or y directions. For each segment oriented along y, there is an energy penalty of $\epsilon$. We also know the end segment is at $(L_x, L_y)...
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1answer
69 views

Calculating energy U from $\partial U/\partial q$

Imagine $N$ oscillators with only two possible energies, $\epsilon_0$ and $ \epsilon_1$, with $\epsilon_1 > \epsilon_0$. Taking $\epsilon_0 = 0$ for now I showed $\Omega(q\epsilon_1) = \frac{N!}{(...
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1answer
295 views

Canonical partition sum for two fermions in harmonic potential

In an old exam, I found the following problem: Two Particles in a potential well We look at a onedimensional harmonic potential well that hold two spinless particles that do not interact with ...
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336 views

Why does $S = k_B \ln W$ not always apply?

I thought for a long time that the Boltzmann formula for entropy, $S = k_B \ln W$, was a universally true statement, or rather the definition of entropy from the perspective of statistical mechanics. ...
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1answer
189 views

Infinite heat capacity or susceptibility means fluctuation on all scales

I remember reading in an introductory text to phase transition (sorry I don't remember the name) that at a second order phase transition the specific heat and the magnetic susceptibility become ...
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658 views

When to use the Boltzmann distribution and the chemical potential?

How do you know when to use the Boltzmann distribution for a particular problem? I have many polymers connected together in many different possibilities by connector agents. All are in a solvent. I ...
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109 views

Some questions about the large-N Gross-Neveu-Yukawa model

Consider the following action with a fermionic field $\psi$ and a scalar field $\sigma$, $S = \int d^dx \{ -\bar{\psi}(\gamma^\mu \partial_\mu +\sigma )\psi + \Lambda^{d-4}[ \frac{(\partial_\mu \...
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1answer
103 views

Spin version of Maxwell's demon: Where's the energy?

I have confused myself about the following variant of Maxwell's demon and I can't seem to find out where the energy went. Consider this: You have a chain (one dimension) of spins (up/down) with a ...
4
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1answer
114 views

(Euclideanized) QFT on $S^d$ vs $S^{d-1}\times S^1$

Broadly I would like to understand what is the difference in the physical interpretation of a (Euclideanized) QFT which is on space-time $S^d$ and which is on a space-time $S^{d-1}\times S^1$. In ...
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1answer
235 views

What is the difference between thermodynamical equilibrium and statistical equilibrium?

I am trying to understand what is the different between thermodynamical equilibrium and statistical equilibrium, for example, between photons and electrons at the early universe. (I read through paper ...
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759 views

Temperature; Why A Fundamental Quantity?

Temperature is just an indication of the combined property of mass of the molecules and their random motion. We can explain no effective energy transfer between two conducting solid bodies in contact ...
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1answer
138 views

Relation between a Quasistatic and a reversible process

Why is it that if a process is reversible, it is quasi-static? Does it mean that then the process is also non-dissipative if it is quasistatic?
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1answer
723 views

About Boltzmann H-theorem

What is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize ...
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1answer
179 views

Prefactor for phase space integration

When calculating the canonical partition sum, we had the following: $$ Z_\text C = \sum_{\vec p} \sum_{\vec x} \exp(-\beta H(\vec p, \vec x)) $$ Now, since $\vec p$ and $\vec x$ are pretty much ...
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1answer
60 views

Maximising entropy when energy is shared between systems

This is a problem to do with statistical physics, and the exchange of energy when we have two microcanonical ensemble. I don't understand why there should be a minus sign in the middle, if Energy* is ...
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0answers
117 views

Motivation of the Heisenberg model of ferromagnetism

In the Heisenberg model of ferromagnetism the atoms are assumed to be arranged in a lattice. The $i$-th atom has a spin operator $\vec S_i$ (here $i$ belongs to the lattice). The Hamiltonian is given ...
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2answers
2k views

If quantum gas goes below 0K, is calling 0K absolute zero irrelevant?

Lord Kelvin defined the absolute temperature scale in the mid-1800s in such a way that nothing could be colder than absolute zero. Physicists later realized that the absolute temperature of a gas is ...
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3answers
881 views

Boltzmann–Gibbs-distribution as resulting from a limiting density of states?

I'm interested in the relation between the probability distribution $p_i$ over states of a system on the one side and the density of states $\rho(\eta)$ of its environment. (Meaning, $\int_{\eta_a}^{\...
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1answer
380 views

“Pressure - Average Energy” ratio of ideal quantum gas?

Classically, one can easily show the following relation using a straightforward canonical ensemble computation for a non-interacting gas: $$\frac{PV}{\langle E\rangle}=\frac{2}{3}$$ Now, apparently ...
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1answer
40 views

A condition for relative gas

Consider an ideal gas in a box. we know (no matter what, right?) that each massive particle's energy holds $E^2=c^2p^2+m^2c^4$ . how come that the condition for that gas to be relativistic is $E\...
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2answers
176 views

Bolzmann entropy [duplicate]

The Boltzmann entropy is defined as the logarithm of the phase space volume (E). Is there a reference, book, paper which shows where this definition comes and how it is equal to the phase space ...
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1answer
676 views

Connection between Kolmogorov entropy and Boltzmann entropy

http://math.stackexchange.com/questions/527384/what-is-the-connectivity-between-boltzmanns-entropy-expression-and-shannons-en mentions a relationship between Shannon entropy and Boltzmann entropy. Is ...
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2answers
410 views

Statistical Entropy and Information theory

I am having trouble in understanding the following concepts : Pg 231 Appendix B of the link http://books.google.ca/books?id=lEu7CTGjdDkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#...
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0answers
369 views

Free Energy of N Spin 3/2 Particles

This question is from the book "Introductory Statistical Mechanics" by Bowley and Sanchez. The question is as follows: Calculate the free energy of a system with N particles, each with spin 3/2 with ...
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1answer
165 views

General Thermodynamic equation of state

I heard my professor saying that the equation $$ PV = \frac{2}{3}U $$ is valid for any non-relativistic gas, be it Ideal or Real gas(includes quantum ideal gases). Is this true, If it is how can we ...
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43 views

Flammability and statistical mechanics

I am wondering to what extent the flammability can be predicted from the statistical properties of an ensemble. Given the partition function of an ensemble, can we in principle predict this property? ...
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2answers
79 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 ...
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2answers
286 views

Phonon mode in canonical and grand canonical ensemble

I derived the averaged energy for phonon mode with frequency $\omega$ in canonical ensemble and in grand canonical ensemble. Averaged energy derived in canonical ensemble is $E_c=\frac{1}{2}\hbar\...