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

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Physics of tagging at B factories

At some B factories, mesons carrying $b/\bar{b}$ quarks are created by $e^-e^+$ collisions at $\gamma(4S)$ resonance. $\gamma(4S)$ decays into antisymmetric wavefunction given by $$ \frac{1}{\sqrt{2}}...
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48 views

How many particles are in the first excited state of Bose gas below critical temperature?

When Bose gas it cooled below critical temperature some of it condenses into Bose-Einstein condensate, resulting in seemingly infinite occupation of 0th state because $\mu = 0$. In reality, the 0th ...
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36 views

Problem on probability expectation value

I have go through a lesson of classical probability and it is the no. of trial divided by the total number. And I have already read the three types of probability distribution such as Binomial ...
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1answer
32 views

The effects of heat and work on a system

I am unable to grasp the following statements which I found in the literature. For a closed system (no transfer of matter), heat in statistical mechanics is the energy transfer associated with a ...
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29 views

3-state Potts model - probability of finding a site in state 1

Question: Consider the 1d 3-state Potts model of N sites (i.e., each site can be in either state 1, 2 or 3). Find the partition function and the probability of finding a site in state 1, $< \frac{1}...
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19 views

Microcanonical Ensemle [closed]

The energy of a particle is given by E=|p|+|q|, where p and q are generalized momentum and coordinate respectively. All the states with E less than equal to E0 are equally probable and states with E ...
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66 views

Why is intensity related to number of photons?

I have been reading up on Doppler broadening and have found a number of sources (for example here and here) which seem to be taking the number of photons in the range $[\nu,\nu+d\nu]$ to be the same ...
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64 views

Fluctuation-dissipation theorem and Kramers-Kronig relations

Is there any connection between fluctuation dissipation theorem and Kramers-Kronig relations? They are often described together under "Linear response theory" but I do not see any exact connection (...
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268 views

Imaginary Part of the Free Energy - Sohotski Plemenj theorem

I have posted this question already on Math Stack Exchange and I hope not to annoy the community if I post it here again, looking maybe for a better suited audience. I need to understand how the ...
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1answer
37 views

Free particle partition function in microcanonical ensemble

From M. Tuckerman, Statistical Mechanics, 3.5 The free particle and ideal gas It is said that the 1D free particle would have partition function $$\Omega = \frac{E_0L\sqrt{2m}}{h\sqrt{E}}$$ where $...
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155 views

Thermodynamic equilibrium or thermal equilibrium and equipartition theorem

In all derivations of the equipartition theorem I can find a thermodynamic equilibrium distribution is used to show it's validity. But more vague sources (physics.stackexchange answer by Luboš Motl, ...
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35 views

Meaning of $\frac{1}{\beta} \frac{\partial \ln{Z}}{\partial X}$ in arbitrary ensembles with X being a sharp Observable of the System

I often find the statement, that for an arbitrary ensemble with Observables $O_i$ of which only the mean value is known, and $\tilde{O}_j$ that are known exactly, the partition function $Z_{\vec{\...
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67 views

Is the pressure-gradient force an entropic force?

A gas flows from an area of high pressure to an area of low pressure when there are no other forces preventing it. From a macrosopic perspective you have to infer that an underlying force is ...
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66 views

What should I think of a diverging beta function (in Renormalisation Group flow)?

I have written a set of RG flow equations using Functional Renormalisation Group methods. I am looking at the flow of a well known problem with an additional original coupling. I did not do anything ...
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1answer
30 views

Adibatic process in QM and thermodynamics?

I have come over the phrase 'Adiabatic process' in two different contexts, that of QM and Thermodynamics . QM A adiabatic process is one is slow compared to: $$t=\frac{\hbar}{E_n-E_m}$$ and ...
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63 views

What does the solid phase in a two-dimensional system with Lennard-Jones potential look like?

Consider a system of two dimensional particles interacting via Lennard-Jones pair potential: $$u(r) = 4[(\frac{1}{r^{12}})-(\frac{1}{r^{6}})]$$ where r is the distance between two particles. What does ...
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87 views

The temperature of an electron

Does an electron have a temperature, if so, what is it? Imagine an electron (Ke = 1 eV) in a tube at room temperature (300 K) what is its temperature? Imagine now same electron in space (3 K) ...
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88 views

Deriving Enthalpy from Stat Mech

One can derive all the numerous thermodynamic potentials (Helmholtz, Gibbs, Grand, Enthalpy) by Legendre transformations, but I'm interested in seeing each from Stat Mech instead (ie taking the log of ...
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57 views

The average value of the electric polarization of an ideal gas

An ideal gas consisting of $N$ molecules possessing an electric dipole moment $\mathbf{d}$, placed in a constant electric field intensity $\mathbf{E}$. Need to calculate the average of magnitude of ...
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52 views

Deriving equipartition the (Sin Itiro Tomonaga ) way

In his book on quantum mechanics Tomonaga derives the equipartition law or energy using this integral. I am having several doubts on solving this integral! Is this solvable via this method?
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38 views

Is Thermalization of a subsystem simply the result of Decoherence of its state?

I would appreciate answers that explain both the concepts in short to underline if there are any key differences between the two. Also, how does a localized state survive decoherence?
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13 views

Pearson correlation of neural responses with it's linear estimation

I am trying to anderstand the following fact: Suppose I have a linear estimation of a stimulus: $ \hat{s} = \mathbf{w}^T(\mathbf{r} - \mathbf{f}(s_0)) + s_0$ where $\mathbf{w}$ is a vector of ...
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36 views

Implications of Indistinguishability of Particles

Wikipedia comments here on the effects of indistinguishibility of particles. Namely, it talks about the distribution of states after allowing the system (here two two level systems) interact and ...
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25 views

What are some good books on foundations of Thermodynamics [duplicate]

I am not looking for some introductory texts, graduate text, etc. I am looking for something that addresses to foundational problems in thermodynamics and statistical mechanics.
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59 views

What Statistical Mechanics does in classical regime

In a book of Dipankar Home, "Foundations of Quantum Mechanics", he has mentioned that A newer theory should not only predict all the results that are already predicted by it's predecessor where ...
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87 views

Approximate expression for the ground state of hopping Hamiltonian

In second quantization, the Hamiltonian describing the hopping process between two neighboring sites is given ($N$ - number of particles and $M$ - number of sites) by: $$\hat{\mathcal H} = J\sum\...
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Is there an established theory on statistical physics in curved spacetime?

I tried to check this in google scholar but didn't find a paper explicitly focused on this topic. Do anyone know of some references on this issue? I do not mean the thermodynamics in curved spacetime ...
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Numerically extracting free energy in renormalization procedure

I have some doubts about how to apply real space renormalization numerically. I understand the theoretical concept, and how we require $Z'=Z$, being $Z'$ the partition function of the renormalized ...
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1answer
60 views

Difference between semi-classical Maxwell Boltzmann Statistics and Boson Statistics

Since semi-classical MB assumes the indistinguishability of particles and Boson Einstein statistics similarly treats degenerate states as indistinguishable states. What is their difference when ...
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105 views

Difference between throtling and adiabatic expansion

Throttling process is an isoenthalpic process.$$U+PV=constant.$$ during throttling process does the gas do work at the cost of internal energy such that its temperature decreases? Then what is the ...
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132 views

Thermal average, thermal fluctuations

I've a doubt concerning the physical meaning of "thermal average" and the "thermal fluctuation" in the canonical ensemble. Let's consider a very simple thermodynamic system: N particles, at fixed ...
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1answer
20 views

Average value of Force in rotating bead using statistical physics

Consider a mass m fixed to the middle point of a string of length $L$ whose extremities are a distance $$l$$ apart, and pulled with a tension $$F$$. The system is in thermal equilibrium, and one ...
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27 views

Magnetisation of a degenerate electron gas in a weak field?

So I am looking at Landau's and Lifshitz's "Statistical Physics, Part I" chapter on degenerate fermi gases and specifically at chapter on Pauli's Mangetism or magnetism of degenerate electron gases, §...
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27 views

Expansions of Bose Functions

To study the thermodynamic behavior of the limit $z\rightarrow$ 1 it is useful to get the expansions of $g_{0}\left( z\right),g_{1}\left( z\right),g_{2}\left( z\right)$ $\alpha =-\ln z$ which is ...
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75 views

Chemical Potential in the canonical and grand canonical ensemble

I'm studying the ideal Fermi gas from "Statistical Mechanics", by R. K. Pathria. In particular, the following formula, which can be found on page 237: \begin{equation} \mu=\left(\frac{3N}{4 \pi g V}\...
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30 views

Computing Maximum Heat Capacity

I've encountered a problem in my statistical mechanics class that I'm not sure I'm approaching correctly: Consider a system of N interacting spins. At low temperatures, the interactions ensure that ...
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3answers
118 views

How can we define a velocity for quantum objects?

I have a question about quantum mechanics: I know that velocity is defined as the change of position with time, $v = \frac{\mathrm{d}x}{\mathrm{d}t}$. In quantum mechanics, the position of a particle ...
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58 views

Detailed balance of an energy function

I'm having difficulties understanding a problem about the acceptance rules for a given energy landscape. The Problem Suppose a system in which the energy is a function of x only: $$ e^{-\beta U(x)} =...
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1answer
50 views

Adiabatic transition from superfluid to Mott insulator?

I have a question about the dynamical passage from superfluid to Mott insulator state in the Bose-Hubbard model. Is it possible to go from superfluid region to the Mott insulator by changing the ...
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32 views

How to calculate the critical temperatures of noble gases such as He, Ne, and Ar?

It seems like Lennard-Jones potential should be used to calculate the critical temperatures of such noble gases. But I'm not sure how to actually do it. Could anyone give me some ideas or suggestions ...
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Why is entropy additive?

Although it seems simple, I can't get the derivation correct. Here is my reasoning: $P(S)=P(A)P(B)$ Where P is the probability and S, A, and B denote different systems. $S_A=-P(A)\ln P(A)$ and $...
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1answer
74 views

Derivation of Fermi-Dirac Distribution

How can I derive the Fermi-Dirac distribution function using simple mathematics? I am now tired of looking for the derivation on the net.So please help me to understand how actually electrons are ...
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1answer
53 views

Statistical Mechanics problem regarding the enthalpy and the expected value of energy

So I have an assignment(relating to a chapter on Canonical Ensemble) here with $H_E = \langle H\rangle$ where $H_E$ is the enthalpy, and $\langle H\rangle$ is the average of the Hamiltonian, I think. ...
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1answer
70 views

How to represent a Liouville projection superoperator in Hilbert space?

Is there a general way to represent a Liouville projection operator in Hilbert space, or can they take on any form so long as they satisfy the required properties of a projector? e.g. The thermal ...
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2answers
109 views

Why is the interaction energy of a dipole and a magnetic field *negative* when they are parallel?

The interaction energy between a magnetic moment, $\mu$, and an applied magnetic field, $B$, is given by $$\varepsilon=-\mu \cdot B$$ That negative sign is confusing my inuition. If we expand the ...
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24 views

Perodic boundary conditions vs Dirichlet?

I have been working through several examples recently involving particles in boxes (when finding the partition function of an ideal gas for example or looking at photon gases). I have seen two ...
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1answer
63 views

Why does the expansion of gas into a vacuum mean that we have less information about the system? (entropy)

I'm reading through Statistical Physics by F. Mandl and in the chapter about the 2nd law of thermodynamics he states that: The basic distinction between the initial and final states in such an ...
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How to justify the entropy maximum postulate using Statistical Mechanics?

The entropy maximum postulate states that given a thermodynamic system there's a function $S$ of the extensive parameters called entropy which has the property that once a constraint is removed the ...
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1answer
85 views

Density of states in a system of interacting electrons

When we are introduced to the density of states in typical band-theory problems we neglect interaction between electrons, and thus we define the density of states of a sigle particle as: $D(E)=2\int_{...
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65 views

Brillouin function - Classical Limit

The Brillouin function, defined as $$B_j(x) = \frac{j+1/2}{j} \coth\left(\frac{j+1/2}{j} x\right) - \frac{1}{2j}\coth\left(\frac{1}{2j} x\right),$$ tends to the Langevin funcion $$ \mathcal{L}(x) =...