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

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466 views

Why do pressure and chemical potential depend on temperature, instead of having symmetric definitions?

I'm following an introduction to statistical mechanics and have seen the following definitions for fundamental temperature, pressure and chemical potential respectively: $$\frac{1}{\tau} := \left( ...
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1answer
853 views

Practical difference between canonical and grand canonical ensembles

I'm currently doing some calculations which require evaluating various standard thermal expectation values in the canonical ensemble (both bosons and fermions). Now, in order to make my theoretical ...
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2answers
131 views

Grand canonical ensemble with interaction, simulation doubts

First of all, this is a follow-up of my first question. The idea is the same, every state would consist of some particles in a line (with an energy associated) and the particles can not be nearer than ...
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1answer
751 views

Definition of phase transitions in statistical mechanics

Phase transitions in statistical mechanics are usually taught by working through a bunch of examples. I decided to try and think about them from a more "fundamental" point of view - but I've run into ...
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1answer
1k views

What is off-diagonal long range order in superfluid?

From Wikipedia: [...]Off-diagonal long-range order (ODLRO) [...] exists whenever there is a macroscopically large factored component (eigenvalue) in a reduced density matrix of any order. How to ...
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1answer
500 views

Rate of effusion in kinetic molecular theory?

According to the kinetic molecular theory obeying Maxwell-Boltzmann distribution of speeds, the rate of effusion through a pinhole of area $A$ is $$R=\frac{PA}{\sqrt{2\pi M R T}}$$ where $M$ is the ...
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203 views

detailed balance in the context of the ising model

I am having a very basic problem understanding the idea of detailed balance, particularly in the context of the Ising model. Most references I have found contain the following phrase: "In ...
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86 views

Can the correlation for the Potts model be bounded?

I am studying a $d$-state Potts model. A configuration $\sigma$, which assigns for each $x\in \mathbb{Z}^2$ a value $\sigma(x)\in [1,2,\ldots,d]$, with the probability on a finite lattice defined as ...
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261 views

Any open areas to work in non equilibrium thermodynamics for a Phd student? [closed]

I see that many papers written on fundamentals of thermodynamics(theory) nowadays are by some old professors somewhere(there may be exceptions). Most active young faculty don't seem to be seriously ...
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170 views

Is “detailed balance” equivalent with a continuity equation in state space?

I have a talk tomorrow in which detailed balance is needed and I don't want to bore my audience with elaborate explanations for it so I'm looking for simpler explanations. As far as I understood it ...
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1answer
175 views

Research on ground state configuration of Ising model

I want to do mathematical research (algorithm construction and mathematical analysis) on Ising model ground state configuration. From what I know, the state of art research is using graph theory ...
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4answers
685 views

Entropy as an arrow of time

From what I understand, entropy is a concept defined by the experimentalist due to his ignorance of the exact microstate of a system. To say the number of accessible microstates $W$ of the universe is ...
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2answers
372 views

Casimir effect as an entropic force

When I first learned about the depletion interaction, my initial reaction was that it looks very similar to the Casimir effect. On making this remark to the professor, he replied somewhat mystically: ...
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1answer
716 views

Calculating the ideal mixing entropy using Gibbs' entropy formula

Two distinguishable gases are in separate volumes $xV$ and $(1-x)V$ $(x\in [0,1])$ respectively, and the number of particles on each side is $xN$ and $(1-x)N$ respectively. The volumes are separated ...
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1answer
145 views

Boltzmann distribution with interaction between particles?

First of all, I would like to apologize in advance if I make stupid mistakes. I am a mathematician and I am trying to apply the Boltzmann distribution to places where I am not sure if it is applicable ...
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1answer
316 views

A thermodynamic transformation that can be represented by a continuous quasistatic path in its state space may still be irreversible. Why?

A thermodynamic transformation that has a path (in its state space) that lies on the surface of its equation of state (e.g., $PV=NkT$) is always reversible (right?). However, if the path is a ...
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1answer
668 views

Should entropy have units and temperature in terms of energy? [duplicate]

I've been thinking about entropy for a while and why it is a confusing concept and many references are filled with varying descriptions of something that is a statistical probability (arrows of time, ...
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2answers
1k views

Must a reversible engine be a carnot engine?

I have this homework question: "Show that any reversible engine operating between T1 and T2 is a carnot engine." I think I have a solution, but it feels very hand-wavy. We know that any process that ...
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3answers
559 views

What is the energy of a standing EM wave? Is it probabilistic?

In a cavity, the standing wave will constructively interfere with itself, so its energy gets higher while the oscillator is still vibrating. Since the vibration time is not a constant value, and ...
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1answer
69 views

Can a distribution with sharper energy maximum than the exp-function give an equivalent theory?

Because for many particles the distribution $\varrho\sim\mathrm e^{-\beta\ H}$ has an extremely sharp maximum, the expectation values of the canonical ensemble agrees with that of the microcanonical ...
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0answers
40 views

Ergodicity Breaking in Supercooled Liquids

What is a ergodic system? What is Onset temperature of ergodicity breaking in super cooled liquids when we go towards lower temperature?
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1answer
311 views

How to derive the two-term approximation for the Boltzmann equation?

Starting with the Boltzmann equation in terms of $f(t,\vec v,\vec x)$ or $f(t,\vec v)$ http://en.wikipedia.org/wiki/Boltzmann_equation $$\left(\frac{\partial}{\partial t} + \vec{v} \, ...
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1answer
235 views

Entropy of a particle with two energy states [closed]

A particle has two energy states having energies $E_0$ and $E_1$ with degeneracies $g_0$ and $g_1$. The respective probabilities are $p_1$ and $p_2$. What is the entropy in terms of $p_1$, ...
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1answer
251 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 ...
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2answers
533 views

The statistical nature of the 2nd Law of Thermodynamics

Ok, so entropy increases... This is supposed to be an absolute statement about entropy. But then someone imagines a box with a 10 particle gas, and finds that every now and then all particles are in ...
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46 views

What is Verlinde's statistical description of gravity as an entropic force? [duplicate]

What is Verlinde's statistical description of gravity as an entropic force leads to the correct inverse square distance law of attraction between classical bodies?
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77 views

Can classical orders coexist with quantum orders?

For example, the ground state of the antiferromagnetic(AFM) Heisenberg model $H=J\sum_{<ij>}\mathbf{S}_i \cdot \mathbf{S}_j(J>0)$ on a 2D square lattice is a Neel state, which is a classical ...
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1answer
368 views

Why do humans like to break the second law of thermodynamics? [closed]

Roughly speaking, Entropy is a measure of the disorder of a system. However as humans, we tend to do the complete opposite. For instance, in a home if a painting that is hanging on the wall is ...
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1answer
643 views

Ensemble of harmonic oscillators

I have some problems with problem 2.3 from Reif's Fundamentals of statistical and thermal physics: Consider an ensemble of classical one-dimensional harmonic oscillators. a) If we assume ...
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1answer
401 views

Are there any modern textbooks on statistical mechanics which don't ignore Gibbs' analysis of the microcanonical ensemble?

I have lately been reading Gibbs' book Elementary Principles in Statistical Mechanics, and I'm surprised how much in that book seems to have been ignored by later textbook writers. In particular, ...
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0answers
64 views

Random orientation percolation (Grimmett model) from the viewpoint of statistical mechanics

This is a rather soft question, but I would like to know how physicists would approach a problem which seems to be hard from the mathematical prospective. The Grimmett percolation model is defined ...
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0answers
65 views

What is ``thermal" about a thermal quotient of EdS and EAds?

This is in continuation of my previous question and is in reference to this paper. I guess that the authors are interested in $S^n$ and $\mathbb{H}^n$ since these are the Euclideanized versions of ...
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2answers
609 views

Why is a hard sphere gas correlated?

In stat mech we calculated the radial distribution function (a.k.a. pair correlation function) for a classical gas by using perturbation theory for the BBGKY hierarchy. (I could post more details of ...
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301 views

Probabilities in statistical mechanics

I am reviewing some concepts in statistical mechanics and am becoming confused with how to calculate probabilities when a system has $N$ non-interacting particles. For instance, let's say we have ...
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1answer
67 views

what molecule would have molar entropy $R \ln 2$ at $0K$?

I was browsing my friends old notes and I came across the following problem that I am not sure if it's correct. Q. Prove that the molar entropy of CO of $0K$ would be $R \ln 2$. Here, it is ...
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1answer
343 views

volume of phase space of composite microcanonical ensemble

Let $N_1$ be number of particles in volume $V_1$ with momenta and coordinates $(p_1, q_1)$ and $N_2$ be particles with momenta and coordinates $(p_2, q_2)$ in $V_2$, if $E_1, E_2$ be the energies of ...
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0answers
39 views

What is the lifetime of an induced magnetization in a para/diamagnetic material?

To the best of my knowledge thermal fluctuations are responsible for washing out any effective magnetization, once the external field is switched off. Since thermal fluctuations need some time to ...
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2k views

When is temperature not a measure of the average kinetic energy of the particles in a substance?

I had always thought that temperature of a substance was a measure of the average kinetic energy of the particles in that substance: $E_k = (3/2) k_bT $ where $E_k$ is the average kinetic energy of ...
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1answer
114 views

Explanation Needed: Thermodynamics of a hot/cold water jet machine

I didn't know where to begin with this problem. I eventually found a solution online, which is why I'm reposting this question with an answer. I was wondering if anyone can explain the one question I ...
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1answer
479 views

Why is velocity normally distributed in a gas, but not energy?

If one looks at a cubic box of gaseous atoms all initially flying in the same direction at the same speed (but flying at an angle to the walls, so as not to reflect up-and-down against the box walls ...
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1answer
208 views

Derivation of Pressure/Kinetic Therory problem involving hole in box

A box of volume $V_0$ has a small hole of area $A_0$. The box initially has one mole of an ideal gas at $t = 0$, which is at an initial temperature $T (t = 0)$. Find the rate of energy flow through ...
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3answers
132 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 ...
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0answers
64 views

Infinite quon statistics/Quantum Boltzmann statistics: models and hamiltonians

I learned long ago that there are some exotic classes of statistics. One of them is calleq $q$-on or quon statistics. It is given by $$a_ia^+_j-qa^+_ja_i=\delta_{ij}$$ Infinite statistics (Quantum ...
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328 views

Can the laws of classical mechanics be derived from quantum mechanics? [duplicate]

Can classical mechanics be derived from quantum mechanics as the same way thermodynamics derived from statistical mechanics?
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1answer
79 views

Nonequilibrium themal QFT

Wick rotation to thermal of QFT in Minkowski space to thermal QFT, which is after this transformation analogue to statistical mechanics, does only describe equilibrium statistical mechanics. On page ...
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87 views

Is there a systematic way to determine the relevant variables needed to describe a nonequilibrium system?

In strong nonequilirium, the statistical operator describing the system depends on an infinite number of variables (BBGKY-hierarchy), contains information about all the previous states starting from ...
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1answer
125 views

What is the broken-sublattice-symmetry phase in an intermediate temperature of the three-state antiferromagnetic Potts model?

I have just read one paper ( Phys. Rev. E 54, R5885 (1996) ) where it was mentioned that the broken-sublattice-symmetry (BSS) phase was stable in the whole low-temperature region. The BSS phase at ...
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Why do we expect our theories to be independent of cutoffs?

Final edit: I think I pretty much understand now (touch wood)! But there's one thing I don't get. What's the physical reason for expecting the correlation functions to be independent of the cutoff? ...
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258 views

Derivation of differential scattering cross section - off-center target

This is a followup question to this pretty good answer regarding deriving the Boltzmann equation. What if the center of the target particle is actually not the same with the scattering center (or may ...
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0answers
247 views

Peierls Argument for Absence of Long Range Order

I'm really confused about the argument in Cardy's book for why there can't be long range order in 1D for discrete models. Let me just copy it out, and hopefully someone can explain it to me. He ...