# Tagged Questions

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

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### Schwabl states that a change in external parameters cannot increase entropy. If so, how can an adiabatic process be irreversible?

I am working my way through trying to understand statistical physics, and this particular, apparent inconsistency has had me stuck for days. Any help or advice would be hugely appreciated. I was ...
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### Why can we say that $\bar{d}Q=TdS$?

When we introduce entropy we do this by saying that: $$\bar{d}Q=TdS.$$ Now I was wondering why this should be true? I know that by looking at a Carnot cycle, we do get this relation for reversible ...
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### How can we tell if a molecule is in thermodynamic equilibrium from scattering data?

We have a molecule that is emitting/absorbing photons. We know the Hamiltonian and that there are several levels. We count the emitted photons at different angles and frequencies. We can also do ...
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### entropy of a long molecule chain with respect to its length

Consider a (very long) one-dimensional chain of $N$ moleculs, which can be in either of the energy states $\alpha$ or $\beta$. The configurations have length $a$ or $b$ respectively. Show ...
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### How to derive the critical temperature for Bose-Einstein condensation of photon?

I found in Nature magazine that photon can have Bose-Einstein condensation. But I have a question how to derive the critical temperature for photon? Because the chemical potential of photon is zero ...
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### What is the conceptual difference between Gibbs and Boltzmann entropies?

In simple words what is the conceptual difference between Gibbs and Boltzmann entropies? Gibbs entropy: $S=-k_B\sum p_i\ln p_i$ Boltzmann entropy: $S=-k_B\ln \Omega$
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### How did Kelvin make this fascinating calculation?

I was just reading Lord Kelvin's "The Sorting Demon Of Maxwell" where I found this quote concerning what Maxwell's Demon can do: (He) can direct the energy of the moving molecules of a basin of ...
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### Difference between heat and work

According to the Kinetic Theory of Matter, temperature is nothing but a measure of the kinetic energy of matter. My textbook says that the change in internal energy of a system is the heat gained plus ...
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### Why is the canonical partition function the Laplace transform of the microcanonical partition function?

This web page says that the microcanonical partition function $$\Omega(E) = \int \delta(H(x)-E) \,\mathrm{d}x$$ and the canonical partition function $$Z(\beta) = \int e^{-\beta H(x)}\,\mathrm{d}x$$...
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### Physical meaning of coefficient of variation

While doing a course in statistical physics I came across a term called coefficient of variation. Now according to Wikipedia, coefficient of variation shows the extent of variability in relation ...
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### When would the Gross-Pitaevskii equation break down as $a\rightarrow \infty$?

It is now common to use Feshbach resonance to tune the s-wave scattering length of a Bose-Einstein condensate. Apparently as $a\rightarrow \infty$, the GPE would break down. The reason is that it ...
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### List of known universality classes

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical ...
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### Pauli's exclusion principle? [duplicate]

What is the idea behind Pauli s exclusion principle? Why should an electron or any particle having non integral spin obey this principle?
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### How do we find the canonical ensemble density matrix for two spins?

A compound system is constructed by two coupling spins, and the Hamiltonian is $$\hat H = -J\hat\sigma_1·\hat\sigma_2 - \mu_\mathbf{B}\big( \hat\sigma_{1z}+\hat\sigma_{2z} \big)B.$$ So, how ...
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### Simple estimation of the critical temperature of water

I'm trying to develop fermi estimation skills and I came up with a question for which I don't even know where to start from. Here goes: Is it possible to estimate the critical temperature (say in ...
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### Is the stability matrix of a linearised RG flow always diagonalisable?

This is a follow up on "Why are the eigenvalues of a linearized RG transformation real?". My question is simple: Is there some physical (or mathematical) reason for the stability matrix of ...
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### Why are the eigenvalues of a linearized RG transformation real?

The RG transformation $R_\ell$ maps a set of coupling constants $[K]$ of a model Hamiltonian to a new set of coupling constants $[K']=R_\ell[K]$ of a coarse-grained model where the length scale is ...
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### How can entropic effects be prevalent at low temperatures?

I read in a book that at low temperature the hydrophobic effect (for example) is entropic but at high temperatures it is enthalpic. I thought that entropy should decrease at very low temperatures. ...
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### Helmholtz free energy from a relation for entropy

The Legendre transformation defines the helmholtz free energy (at least according to my lectures) as: $F(T,V,N)=E-TS$ It also says to start with $E(S,V,N)$ and $T=\frac{\partial{E}}{\partial{S}}$ ...
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### Why does the Metropolis algorithm allow changes even for ∆E > 0?

In the Metropolis Monte Carlo algorithm, why can you accept changes even for ∆E > 0 (provided that a random number is less than a given probability ratio, e.g. exp(-β∆E))?
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### Definition of entropy in nonequilibrium states

Thermodynamical definition of entropy $$S(p)=-\int p\ln p~dx$$ is defined only on equilibrium system. But why can't we use it for non-equilibrium system? Is there a well-accepted definition for it?
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### Spontaneity / Free Energy of Non-Isothermal Process

I'm trying to determine a lower bound for the work input necessary to make an entropy-reducing process "spontaneous" in the sense that the 2nd law is not violated. For a constant temperature and ...
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### The BBGKY Hierarchy

The collision term in the Boltzmann equation can be derived from the BBGKY hierarchy. Wikipedia says: In statistical physics, the BBGKY hierarchy [...] is a set of equations describing the ...
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### Statistical mechanics: What is a “microscopic realization” of a system?

What is a "microscopic realization" of a system? The context is statistical mechanics. The microscopic system consists of many atoms (too many to track individually) with an assigned probability ...
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### Question about Metropolis Monte Carlo in the case of equal energies

If configuration A is equal to configuration B in a Metropolis Monte Carlo method, do you still do the attempted update?
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### Statistical mechanics: Meaning of “accessible” in “accessible microstates”

What does "accessibility" mean in statistical mechanics? Is it an equivalent concept to accessibility in mathematical control theory? I'll provide an example: When two systems A and B interact on a ...
I am reading through a paper. A tubular membrane, submitted to tension $\sigma$ acting as a Lagrange multiplier to conserve area, fluctuates around a cylindrical shape of length L and radius R. ...