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

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Thermodynamic transformation

Why it is so that any reversible thermodynamic transformation is quasi- static ? Also, Why the converge is not necessarily true ?
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Relation between master, Fokker-Planck, Langevin, Kramers-Moyal and Boltzmann equations

I'm looking for the relation between four important equations which we study in stochastic processes in physics. These equations include Master, Fokker-Planck, Langevin, Kramers-Moyal and Boltzmann. ...
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265 views

Maxwell-Boltzmann distribution for transport equations

I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use. As far as I know it should not be the MB distribution for ...
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140 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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2k views

Planck's distribution and Bose-Einstein distribution?

If the application of the Bose-Einstein distribution is in blackbody radiation, then what is Planck's distribution? Are they same? How did Planck know that he should use a Bose-Einstein distribution ...
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421 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
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243 views

Entropy change in an irreversible process between 2 equilibrium state

Calculating entropy change in an irreversible process between 2 states requires computing the change in entropy for any reversible process between the 2 same states, but why? If someone could provide ...
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24 views

How is zonal flow defined and computed?

The transition to turbulence in pipe flow was recently observed to be in the same universality class as directed percolation. This was done by reinterpreting the turbulence and laminar flow in terms ...
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171 views

Calculate the entropy per atom in Bohmian Mechanics

Bohmian mechanics description of a large number of interacting atoms would require a large phase space due to the large number of classical degrees of freedom. The entropy per atom is given as the ...
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31 views

Diffusion of carbon monoxide in air

I have been reading about carbon monoxide online. It is lighter than air; Yet, in the case of fire, most online sources claim it spreads evenly throughout a room. Why is this the case? How is it ...
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23 views

Temperature dependent chemical potential

Chemical potential is determined by the number of electrons in the system and coincides with the Fermi energy at zero temperature. The chemical potential can shift as temperature changes if the ...
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If we had a “perfectly efficient” computer and all the energy in the Milky-way available, what number could it count to?

The idea for this question comes from an example in cryptography, where supposedly 256-bit symmetric keys will be enough for all time to come (brute-forcing a 256-bit key is sort-of equivalent to ...
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56 views

Why thermal conductivity increases with temperature?

what is the molecular mechanism with which thermal conductivity increases by increasing temperature? at least for metals? I know that heat increases the oscillations of the atoms in the crystal. But ...
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41 views

Fermi energy of electron gas with electrostatic interaction

I have been given the following exam question and am unsure how I would go about solving it: Consider the case of a one-dimensional metal, consisting of a chain of $N$ positive charges $+q$ ...
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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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2answers
223 views

In a Monte Carlo NVT simulation How do I determine equilibration

I'm running an NVT (constant number of particles, volume and temperature) Monte Carlo simulation (Metropolis algorithm) of particles in two dimensions interacting via Lennard-Jonse potential ($U = ...
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194 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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136 views

Do gravitational waves have entropy?

We know, according the current understanding of black holes and General Relativity, as well as quantum fields in General Relativity, that black holes have an entropy proportional to the area of the ...
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175 views

Entropy of the cosmological constant and the laws of thermodynamics?

Convention The convention being used is: $ A_{C} = $ The classical variable Premise Consider the following toy-model universe: A universe with a positive cosmological constant. Basic ...
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277 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
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51 views

Noise spectrum of the thermal noise?

If we have a thermal noise generated by Brownian stochastic force $\xi (t)$, it has zero mean value. And its correlation function at temperature T is : \begin{equation} \langle\xi(t) ...
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25 views

What does 'fully excited' actually mean?

In statistical mechanics you often hear the phrases such as 'when the degrees of freedom are fully excited then....'. An example would be the validity of the equipartition theorem. But what is the ...
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181 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
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68 views

Modern textbook on statistical field theory

What is a good textbook on statistical field theory, with an emphasis on applications to non-equilibrium phenomena? I am a final-year undergraduate, have already taken introductory classes in ...
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25k views

First and second order phase transitions

Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article (at the time of writing) starts by explaining that Ehrenfest's original definition ...
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Why should the Fermi level of a n-doped semiconductor be below the one of a p-doped?

In a pn-junction, the difference in Fermi level between the p doped and the n doped regions causes the apparition of a built-in electric field at equilibrium. This electric field goes from the n to ...
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2answers
79 views

Maxwell velocity distribution, in 1D or otherwise

I learned from my textbook that Maxwell's velocity distribution gives: $$v_{rms} =\sqrt{\frac{3kT}{m}}$$ $$v_{avg} = \sqrt{\frac{8kT}{\pi m}}$$ Presumably this is for a three dimensions. This confuses ...
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51 views

Gibbs' Free Energie

What terms are needed to consider to create a rabbit out of nothing and place it in the classroom? Does this caption answer the question?
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145 views

Periodic ground state 1-dim ising model

Good evening! I'm at the beginning of my study about the Ising model and it has been proposed to me this problem: Find all periodic ground-state configuration for the following one-dimensional Ising ...
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50 views

Velocity from the cumulative distribution function of the Boltzmann distribution

I want to get a Boltzmann distribution of the $v_x$, $v_y$ and $v_z$ velocity components (please, notice that the distribution is one-dimensional). To do so, I need the cumulative distribution ...
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43 views

The entanglement is not completely determined by the partition function, i.e., by the usual quantum statistical physics [closed]

In statistical mechanics thermodynamical quantities, say ${\cal Q}$, are computed using partition function $Z$ defined as $Z = \mbox{tr}[\exp(−H/kT )]$. Here $H$ is the Hamiltonian, $k_{B}$ is the ...
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77 views

A conceptual question related to statistical mechanics

Statistical mechanics allows us to consider an ensemble of systems, each of which consisting of only a single particle. Once we write the partition function for the system of one particle, we can ...
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43 views

Which condition is stronger - ergodicity or mixing?

Reading a statistical physics book, I've encountered the following assertion (without further explanations): [..] the presence of dynamical instability makes the trajectory of a system much more ...
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80 views

Understanding Gibbs $H$-theorem: where does Jaynes' “blurring” argument come from?

According to this Wikipedia article, the $H$-theorem was Boltzmann's attempt to demonstrate the irreversible increase in entropy in a closed system starting from reversible microscopic mechanics. ...
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Hindered rotation model for flexible polymers: deriving the Flory characteristic ratio

In the hindered rotation model we assumes constant bond angles $\theta$ and lengths $\ell$, with torsion angles between adjacent monomers being hindered by a potential $U(\phi_i)$. In Rubinstein's ...
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A micro-reversible stochastic process that models transitions between states with variable energies

Suppose we have a system with 3 possible states A, B and C (there could be $n$ states as well) with energies $E_a(t)$, $E_b(t)$ and $E_c(t)$ that vary with time. If our system has a constant finite ...
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40 views

Why is the average thermal velocity 0?

Thermal velocity is the velocity of the free electron due to their random motion. So how is the average value 0?
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227 views

Chemical Potential as a function of Temperature

I have considered an ideal fermi gas. Then, we can obtain an expression for chemical potential as a function of Temperature. I want to understand the physical significance to it or what it really ...
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1answer
23 views

Example of a Carnot machine made of a different physical system than a ideal gas?

Anybody knows an example of a Carnot machine made with any different thing than a gas? For example wire or a magnet. I was wondering that since I read the Kardar's book on Statistical Mechanics. He ...
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37 views

What is the difference between these two expressions for the partition function, Z?

What is the difference between these two expressions given for the partition function, Z? $$Z = \sum_{i}e^{-\varepsilon_i/kT}$$ $$Z = \sum_{j} g_je^{-\varepsilon_j/kT}$$ where each energy level has ...
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179 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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779 views

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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Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms tries ...
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Triangular and Kagome lattice anti ferromagnet at zero temperature

The triangular lattice with anti ferromagnetically coupled nearest neighbour ising spins has a power law ordered zero temperature state at the three sublattice wavevector. Kagome lattice, with the ...
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Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
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Fermi-Pasta-Ulam for the beam equation

The Fermi-Pasta-Ulam numerical experiment is based upon the discrete wave equation, with a small non-linearity added to the forcing term. Does anybody know of similar research performed on the beam ...
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131 views

Obtaining the temperature from Bose-Einstein and Fermi-Dirac distribution

Lets say you are given a distribution function $f(p)$ and you want to define a temperature, $T_f$, for this distribution. (I assume $\mu = 0$.) It is then natural to define a temperature the ...
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5answers
1k views

The Preference for Low Energy States

The idea that systems will achieve the lowest energy state they can because they are more "stable" is clear enough. My question is, what causes this tendency? I've researched the question and been ...
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1answer
759 views

Pauli paramagnetism for electrons with external magnetic field

Apparently it is to be shown that for electrons under an external magnetic field, in the limit as $B\to 0 $ $$ \chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)} $$ ...
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Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...