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

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Linear thermal expansion from statistical mechanics?

I came across a question recently regarding work done by an expanding metal and the origin of the energy used for the work, and most of the responses pointed the person to look more at the enthalpy ...
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24 views

Microscopic Definition of Heat and Work

If I am given a statistical System, then I can define state-variables like Energy, Entropy or other Observables, and then I can (at least for equilibrium states) give the Change of Energy as: ...
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20 views

Constancy of Coefficients of Additive Integrals Throughout Subsystems of a Closed System

I'm studying Landau and Lifshitz's Statistical Physics, Part 1, 3rd edition and am looking for clarification on the following statement, which appears on page 11 in the section on The Significance of ...
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30 views

probability of striking the circular ring by gas molecules

In kinetic theory we use probabilistic case to derive pressure, no. Of molecules having speed c to c+dc or in such cases.and to derive such equations we introduce a term called "SOLID ANGLE" I come ...
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1answer
54 views

Quantum versus classical computation of the density of states

If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy ...
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1answer
45 views

Mean free path in QFT

I'm trying to understand the hydrodynamic approximation of a general QFT when the large $k$ and $\omega$ DOF have been integrated out i.e that at highly enough temperature every non-trivial QFT ...
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13 views

How the degrees of freedom for gas molecules affect energy

It seems a bit unclear to me how degrees of freedom help judge the amount of kinetics energy in the system. from the formula for the energy of molecule ε = u0 + (v/2)kT it can be inferred that the ...
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1answer
900 views

What leads to the existence of critical temperature?

We know that $T_c$ is the temperature above which no amount of pressure could force a gas to liquefy. But why is this? Somehow I don't buy the point that the gas molecules exert too much pressure ...
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1answer
34 views

How to write any partition function?

So I am familiar with the derivation of the partition function for a canonical and a grand canonical ensemble. I have seen definitions of the partition function for some of the quantum counterparts of ...
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1answer
41 views

water stream cut off abruptly; why there will occur sprinkling?

Suppose that water flows with constant velocity $V$ and constant pressure $p$ through a pipe with diameter $d$. Now the pipe is suddenly cut such that the water will splash out of the pipe into the ...
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30 views

How to derive latent heat from the degrees of freedom in an equation [closed]

I am having some trouble solving a question on statistical mechanics, any help? Q: A certain material vaporizes from the liquid phase at 700 K. In both phases, the molecules have three degrees of ...
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30 views

Confusion about the number of micro states and approximating it for large number of particles

Hopefully after reading the meta site, I can now rephrase the question as more relevant to this site, this is a question related to statistical physics: Let us suppose we are given a system with ...
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1answer
83 views

Ultraviolet catastrophe in a classical world

In the real world, the ultraviolet catastrophe doesn't happen because the quantization of photons modifies the classical behavior of light at frequencies comparable to and higher than the temperature. ...
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31 views

Ising model as quantum model?

I've read in a few papers things that use the fact that the $2D$ Ising model can be interpreted as a $1+1$ quantum spin model. I haven't been able to find this description and would like to read about ...
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59 views

Second law of thermodynamics in linear response theory

I am wondering about the appearance of irreversibility in the response functions or equivalently the correlation functions in a statistical mechanics system. The main principle that I have seen where ...
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2answers
195 views

Itô or Stratonovich calculus: which one is more relevant from the point of view of physics?

Langevin equation provides an example of a physical model which involves a differential equation with a stochastic term. Now, I wonder, how should one treat this? When I studied stochastic processes, ...
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1answer
63 views

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 $$ ...
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1answer
44 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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34 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
31 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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0answers
27 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, $< ...
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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 ...
2
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1answer
58 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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48 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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1answer
262 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
28 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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27 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 (this site, wikipedia) state that only ...
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33 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 ...
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1answer
52 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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64 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
28 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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1answer
60 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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2answers
75 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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1answer
85 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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1answer
51 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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1answer
51 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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36 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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1answer
33 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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21 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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2answers
53 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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2answers
80 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} = ...
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41 views

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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0answers
13 views

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
52 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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1answer
66 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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1answer
87 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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26 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 ...