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

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700 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
388 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
744 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
150 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 ...
5
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1answer
320 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 ...
3
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1answer
717 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
573 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
320 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
238 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
261 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 ...
7
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2answers
565 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 ...
0
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0answers
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?
2
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0answers
78 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 ...
1
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1answer
375 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
661 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 ...
15
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1answer
410 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, ...
2
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0answers
66 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
67 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 ...
12
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2answers
621 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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2answers
303 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
70 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
359 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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2answers
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
116 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 ...
4
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1answer
497 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 ...
0
votes
1answer
210 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
134 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
67 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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0answers
336 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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0answers
92 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 ...
2
votes
1answer
128 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 ...
25
votes
2answers
1k views

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? ...
0
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1answer
270 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
249 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 ...
2
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3answers
990 views

Why the free energy is called 'free'?

The free energy, $F$ of a thermodynamic system at a given temperature $T$, is defined as, \begin{equation} e^{-\beta F} = \mathcal{Z} = \sum_{\{configuration\}} e^{-\beta E(configuration) } ...
0
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1answer
83 views

Possible abuse of notation in statistical mechanics

I know that it often occurs that we need to take a derivitive with respect to $\beta$ in statistical mechanics. However, I think it is poor style to use equations with both T and $\beta$ in them ...
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2answers
327 views

Drude theory of electrical conductivity

I was just trying to calculate the electrical conductivity for a Fermi-Dirac distribution and a Maxwell-Boltzmann distribution, and I ended up with the same result: $$\sigma=\frac{ne^{2}\tau}{m}$$ ...
3
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0answers
79 views

Where else in physics does one encounter Reynolds averaging?

Reynolds-averaged Navier–Stokes equations (RANS) is one of the approaches to turbulence description. Physical quantities, like for example velocity $u_i$, are represented as a sum of a mean and a ...
9
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3answers
392 views

Black magic “Hartree” approximation

The question is about an unusual looking version of the Hartree or mean field approximation. The context is several papers I've been reading recently about the out of equilibrium dynamics of phase ...
2
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1answer
120 views

What are the state functions telling me or how are they related to total energy?

I am quite new to thermodynamics and statistical mechanics so this might be an easy question: In thermodynamics you get a bunch of thermodynamics potentials, so as for example enthalpy, internal ...
1
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1answer
198 views

Infinite-range 1D Ising model

The Hamiltonian for this system is given by \begin{equation} \mathcal{H} \{S\} = -H\sum_i S_i - \frac{J_0}{2} \sum_{ij} S_i S_j, \end{equation} where $H$ is the external magnetic field and there is no ...
3
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1answer
548 views

What is a chemical potential good for?

I read that the definition of the chemical potential is, that it is the partial derivative of the Free energy with respect to the number of particles, $$\mu=\frac{\partial F}{\partial N}.$$ ...
5
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1answer
82 views

Meaning of the 'deep lattice limit' and 'shallow lattice limit'?

In condensed matter literature, at many places, the phrase 'deep lattice limit' is used. Please tell what is the deep lattice limit and the shallow lattice limit?
3
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2answers
636 views

1D Ising Model with different boundary conditions

The Hamiltonian for one-dimensional Ising model is given by, \begin{equation} \mathcal{H} = -J\sum_{<ij>} S_iS_j; \quad i,j=1,2,...,N+1 \end{equation} where $<ij>$ denotes that there is ...
2
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0answers
274 views

Phase transitions. Conceptual link of my intuitive notions and definition of Georgii's book in terms of probabilities

In his classic book O. H. Georgii (Gibbs Measures and Phase Transitions) in Chapter 2 p. 28 define the concept of phase transition follows. Definition A potencial $\Phi$ will be said exhibit a ...