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

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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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214 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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22 views

What is “thermal undulation” in the context of lipid bilayers?

What is thermal undulation in the context of lipid bilayers? Is it another word for "thermal fluctuation"?
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1answer
95 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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92 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
156 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
999 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
71 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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0answers
61 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 ...
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0answers
55 views

Weibull distribution

The Weibull distribution probability density is given by: $$f(w,k,\lambda)=\begin{cases}\frac{k}{\lambda}\left(\frac{w}{\lambda}\right)^{k-1}e^{-\left(w/\lambda\right)^k} &w\geq0 \\ 0 & ...
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1answer
75 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
74 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, ...
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1answer
63 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) = ...
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1answer
108 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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1answer
206 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
74 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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3answers
189 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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0answers
67 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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0answers
37 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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0answers
67 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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0answers
43 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 ...
4
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3answers
360 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
75 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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255 views

Ultra-Relativistic Fermi Gas - Chemical Potential and Energy

I tried deriving the expression for chemical potential of a Relativistic Fermi Gas using asymptotic expansion (for large z) in : $$ N = \frac{V}{h^3}4\pi (KT)^3g_s \int \frac{p^2 dp}{e^{p-\nu}+1} $$ ...
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1answer
228 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
84 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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46 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* ...
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0answers
68 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
219 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 ...
2
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2answers
265 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, ...
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1answer
126 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
37 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 ...
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1answer
274 views

Boltzmann entropy and phase space volume

In Huang's book on Statistical mechanism and Statistical interpretation of Entropy, it is not mentioned that $\Omega$ is the phase space volume, but it is the states of the system. So, how does ...
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2answers
141 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
202 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
177 views

Statistical Entropy and Information theory

I am having trouble in understanding the following concepts : Pg 231 Appendix B of the link ...
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0answers
104 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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2answers
106 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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37 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
62 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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100 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 ...
3
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1answer
132 views

Is mean field theory self-consistency analogous to string theory consistency?

My question is vague, so I'm hoping the answers will help me ask more concrete questions and maybe produce some interesting discussion. In mean field theory, say for the Ising model, we treat the ...
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0answers
159 views

Classical regime for Fermi-Dirac and Bose-Einstein gases

I'm studying statistical mechanics, in particular classical regime for Fermi Dirac and Bose Einstein gases. Time average value for occupation numbers in FDBE statistics: $$ \langle ...
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0answers
51 views

What is the probability that all the air ends up in the upper right corner of the room and we suffocate

Since someone commented this on this question(What is the probability of ice in boiling water?), I would like to ask what is the probability that all the air ends up in the upper right corner of the ...
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1answer
109 views

What is the probability of ice in boiling water?

Ice crystals are spatially ordered, and in every randomness there is a low possibility of temporarily order. If given enough boiling water, and sufficient time, could local clusters water molecules ...
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0answers
146 views

What is the physical interpretation of the Papadodimas/Raju mirror operators?

In this paper http://arxiv.org/abs/1310.6335, the authors discuss the firewall problem and contruct so called mirror operators appearing in the correlation function. The key part seems to be (2.6) ...
2
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1answer
163 views

'Fermi-Dirac'-like occupation probability at high temperature

Consider an ensemble of $N\to\infty$ free particles, each of which can assume energy states $E_i\in\{0,E\}$. Using the canonical ensemble one can compute the occupation probability for a single of ...
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1answer
969 views

Partition function for a microcanonical ensemble

Is it possible to write down a partition function for a microcanonical ensemble?
2
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1answer
304 views

Probability of finding n particles in a volume v

I'm trying to calculate the probability of finding $n$ particles in a certain volume $v$ in a system with a total of $N$ particles and total volume of $V$. My problem is that I've tried two approaches ...
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1answer
142 views

Questions about Statistical Mechanics

For grand partition ensemble, is it true that the introduction of chemical potential allows us to have the sum of number of the particles in each state to be the total number of particles ("On ...