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

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Pressure components in a film

I am performing molecular-dynamics simulations of a polymer near a crystalline substrate (polymer film). I am comparing the mechanical properties in the film with the properties in the bulk polymer. ...
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30 views

The relationship between the two statistical mechanical definitions of entropy

It seems like similar questions have been asked here; hopefully my question is not a duplicate. I am reading my textbook on the statistical mechanical definitions of entropy, and I am very confused ...
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31 views

classical and quantum correlation functions

Quantum Field, quantum fluctuation even with no temperature In QFT, the correlation function $<0|\hat{\phi} (x)\hat{\phi} (y)|0>$ describes the fluctuation correlations of vacuum state ...
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50 views

Partition function microcanonical ensemble

I was wondering if there is a way to understand the partition function for a microcanonical ensemble $$\mathcal Z(E)=\sum_{\text{microstate $i$ with energy $E$}} w_i$$ as a limit of the continuous ...
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1answer
18 views

Help Understanding Correlations In Many Particle (Beam) Physics

I am having a lot of trouble looking at the statistical properties and having some sort of intuitive sense of correlations among different properties of many body systems (in particular charged ion ...
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27 views

Bose Enhancement Factor

How may one explain the fact that the probability of a boson transferring to a state with an occupation number n is 'enhanced' by a factor of (1+n), compared to the classical case? (In the classical ...
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50 views

Reduced phase space density

I have a dimensional problem with the single particle phase space density The partition function in the microcanonical ensemble is of course dimensionless Thus $$ \rho ( q, p ) = ...
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69 views

References to Mechanics (Classical, Quantum, Statistical) using Time-Scale calculus?

Time-Scale Calculus, is a theory which unifies ordinary (plus fractional and q-) calculus with discrete (and finite differences) calculus. In a sense, in a similar way the Lebesgue integral (or ...
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1answer
41 views

How to prove $f_1f_2 \rightarrow f_1f_2(1\pm f_3)(1\pm f_4) $ in Boltzmann equation of degenerate gas?

How to prove $f_1f_2 \rightarrow f_1f_2(1\pm f_3)(1\pm f_4) $ in Boltzmann equation of degenerate gas ? I know it's Bose enhancement and Fermi block. I want to know why it's exactly this form? For a ...
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Doesn't entropy increase backwards in time, too?

In statistical explanations of entropy, we can often read about a (thought) experiment of the following sort. We have a bunch of particles in box, packed densely in one of the corners. We assume some ...
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118 views

Ideal gas in ensemble

I want to calculate the phase space density for a single ideal gas particle in a microcanonical ensemble. I know that the partition function is given by the well-known expression that you find for ...
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2answers
33 views

Entropy of ideal gas with finite volume

I know that the entropy of an ideal gas is given by the Sackur-Tetrode equation, but is there also a way to take into account that even the ideal gas will acquire some volume $v_0$? Or is it then just ...
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32 views

Applications of statistical mechanics [duplicate]

I'm trying to learn statistical mechanics on my own. I'm reading about canonical and grand canonical ensemble and I'm making good progress. The problem is that I can't find interesting applications of ...
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72 views

Partition function containing QM?

I am wondering about the partition function of the classical microcanonical ensemble. It contains Planck's constant and also an indistinguishability argument about the particles I am looking at and I ...
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2answers
111 views

What is the connection between the non-reversibility of the decay of unstable nuclei (as Uranium, Plutonium) and the 2nd principle of thermodynamics?

The 2nd principle of the thermodynamics says that if a system (e.g. an ideal gas) is left undisturbed, its number of microscopic states only increases. This is a statement of irreversibility of the ...
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2answers
76 views

Second Law from Statistics

Hi all I hope you can help me with the statistical origins of the Second Law. I cannot find anything that mathematically proves that order from disorder is impossible only improbable Leading me to ...
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1answer
47 views

In statistical mechanics, what does integrating with respect to the position of a molecule mean?

So, this is probably a dumb question, but I cannot visualize or make sense of integrating over the position of a molecule in space. Okay, so an example in my thermodynamics textbook: we have N = 5 ...
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1answer
66 views

Equilibrium in Stat Mech and Phase space density

I was wondering if there is any relationship between equilibrium in Stat Mechanics and the phase space density of a system? This does not seem to be completely independent, as Entropy is maximized in ...
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63 views

Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...
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46 views

Meaning of phase space density

I am trying to understand Liouville's theorem physically. It says that $\frac{\partial \rho}{\partial t} + \{\rho,H\} = 0$. Thus, we have $\frac{d \rho(q(t),p(t),t)}{dt}=0$. I would like to ...
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14 views

Distribution and different ways of distribution

Is "the number of ways of of distributing $N$ things across a fixed set of energy levels the same as "the number of ways a particular distribution can be realised? My book seems to say that $W$ is ...
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30 views

Boltzmann factor predicts arbitrarily large numbers of electrons at high potential?

In deriving the Debye shielding length we are told that the Boltzmann factor for particles of charge $q$ is: $n_{q}=n_{0}\exp(-q\phi/kT)$ If we assume the potential $\phi$ is positive, then the ...
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20 views

Screened potential of charged impurity in a 2-dimentional electron gas

What's the analytical relation of screened potential of charged impurity in a 2-dimentional electron gas?
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68 views

Boltzmann distribution - statistical mechanics

I have just followed a derivation of the Boltzmann distribution which I have never seen before, and I must say it is really intuitive. However I have a question as to how we can think of the Boltzmann ...
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36 views

Is collision in ideal gas because of physical collision or due to repulsion force

Is collision in ideal gas because of physical collision or due to repulsion force when they approach close by?
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33 views

Entropy of this system

We have a system with two energy states $E_0$< $E_1=0$. We also know that state $E_0$ can only take at most $m$ particles. Curently, there are $n<m$ particles in $E_0$. Now, I am supposed to ...
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51 views

validity of Kramers-Kronig relations for all systems

Are Kramers-Kronig relations valid for all physical systems that obey causality? I came across this example http://journals.aps.org/prb/pdf/10.1103/PhysRevB.83.165119 where the authors say that though ...
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26 views

The Debye temperature for diamond

To simplify the calculation, let's assume that the average speed of sound in the diamond is simply $v_s=\sqrt{E/\rho}\simeq1.414\times10^4 \ \text{m/s}$, and the Debye frequency $$\omega_D=v_s\left( ...
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53 views

Energy without temperature

If you know the entropy $S$ of your system. Is there a general way to calculate the internal energy $U$ of your system? So the entropy $S$ is the only thing I know of my system. I have no information ...
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1answer
36 views

The number of states for fermions, bosons, and Boltzman in statistical mechanics

This is related with Equation 8.58 in Kerson Huang's 2nd edition of Statistical Mechanics. The partition functions for the ideal gases are given as $ Q_N (V,T) =\sum_{\{ n_p \}} g\{n_p \}e^{-\beta ...
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1answer
32 views

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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149 views

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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2answers
42 views

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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1answer
49 views

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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67 views

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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47 views

Euler Equation Arbitrary Quantities

I have a question about the Euler equation. For some state I can write down: $$ U = TS - pV + \mu N$$ In this equation $T$, $p$, $V$, and $N$ are directly measurable so they have fixed values. ...
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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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89 views

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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1answer
70 views

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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57 views

Retarded thermal Green function

I'm working with finite temperature field theory, but I'm having problems understanding the retarded Green's function in this formalism. I'm reading Niemi and Semenoff's article "Finite Temperature ...
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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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41 views

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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1answer
71 views

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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1answer
75 views

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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65 views

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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1answer
37 views

Classical limit of non-interacting, relativistic quantum gas (Kapusta/Gale p.8)

I want to understand two equations in "Finite temperature field theory" by Kapusta and Gale on page 8. The partition function is $$ \ln Z = V\int \frac{d^3 p}{(2\pi)^3}\;\ln\left(1\pm ...
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Wigner function vs. backward kolmogorov

We know that a Wigner function is a quasi probability distribution and a backward Kolmogorov equation for a stochastic differential equation (say quantum Lagenvin equation) gives the probability ...
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1answer
44 views

What is an order parameter?

I've seen order parameter used in two different ways. One is to distinguish between an ordered and an unordered phase, like whether the net magnetization is stable or not. The second way is to ...