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

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14 views

Finding liquid/vapor phases of LJ system with Gibbs Ensemble

I've been trying to use the Gibbs Ensemble Monte Carlo method for finding the liquid and vapor phases for a given particle interaction. This method sets up two isothermal subsystems that exchange ...
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153 views

Phase transitions, Landau Ginzburg theory and Symmetry reduction

On one side of critical temperature (usually for $T<T_{c}$), symmetry is reduced w.r.t the symmetry on the other (usually $T>T_{c}$) regime. I heard on the road (near a theoretical physics ...
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137 views

Adiabatic invariant and Liouville's theorem

It appears that many people have tried to show adiabatic theorem from Liouville's theorem, e.g., Li's note, or at least tried to find some relations, e.g., Rugh, Adib and Tong's lecture notes Sec. ...
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17 views

Examples of systems that becomes gibbsian in the thermodynamic limit

My question is related with Tsallis and Gibbs statistics. It is known that for systems that are far from thermodynamic limit or present long-range interactions the Tsallis distribution may be suiter ...
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1answer
25 views

Stability of a system of Brownian particles with non-physical collision

A few months ago I wrote this simulation of a system of circles bouncing off each other. It's a two-dimensional box with elastic balls in it that bounce off each other. I came back to it and noticed ...
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42 views

Partition Function of One-dimensional hard rods

I was trying to follow the derivation presented in the last section, “Isobaric ensemble: an alternative” in the article on one-dimensional hard rods, available on ...
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26 views

Phase-space average equal to the quantum mechanical average in the early universe

I was reading Mukhanov's book of cosmology http://www.amazon.com/Physical-Foundations-Cosmology-Viatcheslav-Mukhanov/dp/0521563984 , specifically about symmetry restoration in the early universe ...
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1answer
26 views

equilibrium state of a system in statistical mechanics

Why we consider the maximum number of micro states or complexions as equilibrium state of a macro state or a system in statistical physics?
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32 views

Extensivity Intensivity and mathematical definitions

Could someone explain how intensivity and extensivity are defined mathematically, I know via their homogeneity as functions of the particle number but how exactly is this done and why? This would ...
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32 views

Change of energy levels in statistical mechanics with heat

Why is it, that energy levels dont change if a system is heated at constant volume? "When a system is heated, the energy levels are unchanged but their populations are changed" If i add heat to a ...
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2answers
82 views

Why do statistical ensembles always fix three variables?

In basic course in statistical (classical) mechanics and thermodynamics, the ensembles used (microcanonical, canonical, grandcanonical, NPT) always assume exactly three variables (n,V,T in canonical ...
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29 views

Usefulness in microstates that belong to the same macrostate?

The number of microstates can be huge, numbers with millions of digits, but they can all represent the same macrostate. IS there any information that can be associated with each microstate ...
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103 views

Ising model at high vs. low temperature

The output of the Ising model over a 2D binary lattice looks to have spin states uniformly distributed over the lattice for high values of the temperature parameter with the output attaining ...
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1answer
42 views

Static structure function for non-interacting Fermi gas

I'm wondering how would one go on about to calculate the static structure function with the ground state being $|\phi_0\rangle$: $S_\vec{q}=\frac{1}{N}\langle ...
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1answer
32 views

Negative amount of particles in a grand canonical ensemble

Knowing that, in the $\mu$-canonical (or micro-canonical) and canonical ensembles, the number of particles is held constant and usually reflects the actual number of particles, in which case $N_{MC} ...
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27 views

Difference between “chemical master equation” and “master equation”

Is there any mathematical difference between "master equations" and "chemical master equations"? Is the chemical master equation in any way more specific than the master equation? I see the former ...
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2answers
54 views

Formation of bonds and heat release

We know when there's formation of bonds during chemical reaction there's heat release to the surrounding due to conservation of energy. But what I am confused about, is the kinetic energy of the ...
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0answers
39 views

How is the probability density function in equilibrium state made equal to a dirac delta function?

While studying statistical mechanics, I stumbled upon the introduction of the dirac delta function in defining the probability density of the microstates and hence the conclusion of equal priori ...
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40 views

Eigenvector distributions, random matrix theory and the ten-fold way

For various applications the distribution of components of the eigenvectors of random matrices is of interest. For example, in the case of a matrix in the Gaussian orthogonal ensemble this ...
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2answers
103 views

The statistical interpretation of Entropy

I recently got introduced to the Statistical Mechanics, particularly, the Statistical Interpretation of Entropy and am utterly confused regarding the following problem: Imagine a box with two ...
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1answer
73 views

Calculated heat capacity different (lower) from experimental value?

When treating gases as ideal, classical systems, the heat capacity can be found by multiplying the number of independent degrees of freedom by 1/2k, where k is Boltzmann's Constant. However, these ...
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3answers
141 views

What happens to the $PV=nRT$ formula as the gas enters the liquid phase?

The formula $PV = nRT$ explains the relationship between pressure, volume and temperature in terms of the quantity of gas present in a container. I'm trying to understand how these are related once ...
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24 views

Partition Function And Macroscopic Properties

In renormalization group transformations, partition function is fixed. My question is which thermodynamic properties are fixed in a renormalization group transformation.
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13 views

Canonical treatment of thermalization of two gases at different temperatures

I'd like to understand the thermalization process when two gases of different species and different temperatures are allowed to mix in an insulated container, interacting only through an elastic ...
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2answers
254 views

Understanding entropy [duplicate]

I am currently doing some research on entropy and I am trying to get my head around the concept. One thing that I am getting right now is that entropy is just an application of probability and ...
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195 views

What is the origin of blackbody radiation? [duplicate]

Of course I know what black-body radiation is, like everyone else who has taken a thermal or statistical physics course. But it was recently pointed out to me that one thing that is rarely taught ...
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1answer
47 views

Confused by Langevin Equation

Trying to understand the Langevin Equation. In particular, this passage from a Wikipedia article has me confused (section: "Thermal Noise in an Electrical Resistor"): $\frac{dU}{dt} ...
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37 views

dependence of braiding matrix element on the fusion product of anyons

In the case of Majorana fermions (MFs), one knows that if one braids MF $a$ with MF $b$, then braiding matrix element $R^{c}_{ab}$ depends on the state $c$ which is the fusion outcome of $a$ and $b$. ...
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96 views

Calculating the number of particles in phase space

I'm looking at the first part of question 7 here (I'm a mathematician trying to self teach some physics, this isn't a homework assignment so I'm just in need of hints)! I'm struggling to make sense of ...
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1answer
52 views

Is kinetic energy related to chemical potential?

I wonder if the kinetic energy written as $\frac{d\mathbf x}{dt}\cdot d\mathbf p$ is related to chemical potential? I ask because if I use $\mathbf p = m \frac{d\mathbf x}{dt}$ as a constitutive ...
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40 views

Probability density function of simple Mass-Spring system

We know that after long run of simple mass-spring system, there should be a probability of finding the mass at certain points between -A and A.. Obviously in probability of finding the particle near A ...
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2answers
223 views

Quantum and Classical Liouville operators

In the Heisenberg picture of Quantum Mechanics, for an observable $\hat{A}$, we have the famous Heisenberg equation giving the time evolution of the operator: ($\hat{H}$ is the Hamiltonian operator) ...
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2answers
110 views

Diffusion of gas into vaccum

I'm interested in solving the diffusion equation for gas in vacuum. I have a general question and a more specific questions. What I know: The Diffusion Equation: For density function ...
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6answers
3k views

How can fast moving particles gain energy from slow moving ones?

Imagine a large diameter piston filled with water connected to a small funnel. When you press on the piston slowly but with considerable force the water will move very quickly from the funnel in form ...
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1answer
32 views

BEC in interacting systems

What is your thought on the following statement: "any system of (weak/ strong) interacting bosons, in liquid phase, will form a condensate at T=0". Any example or counter-example ? Will dimensionality ...
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1answer
123 views

Calculation of long-range forces in Molecular Dynamics - Ewald summation

I am trying to write a code to calculate the potential and forces, for the same using ewald summation.For this purpose, the formula for potential and force I have used is : $$ U = U^{(r)} + U^{(k)} ...
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1answer
180 views

About thermodynamic beta

First of all, I'm not majoring this part and just finding some answer about Arrhenius rate equation: $$ v \propto \exp\left(-\frac{E_a}{kT}\right) .$$ To derive this relation, I started with ...
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1answer
66 views

Is Maxwell-Bolzmann a Normal (Gauss) distribution or a Chi distribution?

I was sure that the Maxwell-Bolzmann was a Normal distribution, but then I read that it was a Chi distribution on Wikipedia.
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2answers
46 views

Energy transfer in form of work or heat?

Suppose a system A which is a vessel of water with two electrodes, connected by a resistor, placed in the water. If you apply voltage to the electrodes, energy is transferred from the battery (not ...
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41 views

Speed of electrons at given temperature in non Hydrogen-like atoms

I may be somewhat confused on the topic, so please excuse me if this is really basic. For the Hydrogen atom, one can easily derive the expectation value of the electron's speed: $$ \langle v \rangle ...
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243 views

What is the physical meaning of a Partition Function in Statistical physics?

In many places in statistical physics we assume the partition function. To me the explanations after partition functions are most of the times clear but always wonder why a partition function and what ...
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2answers
97 views

Langevin Equation - Stochastic Differential Equation. What are the subtleties?

I am trying to find out the motion of a particle in 3D governed by the Langevin equation, numerically. Anyway, the Langevin equation is given by $$m \ddot{x} = -(6\pi a\nu) \dot{x} + F_b $$ where ...
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1answer
40 views

What is meant by the expression “Markovian dynamics”

I know what a Markov chain is but what does it mean in physics when I say that I assume Markovian dynamics? For example in Quantum Mechanics, I read that it means that the time evolution can be ...
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1answer
223 views

Dr. Pierre-Marie Robitaille: On the Validity of Kirchhoff's Law

Lately I've been researching about the black-body spectrum and the historical development of Planck's Law. I mainly wanted to understand a little bit more why many different objects (Stars, Hot ...
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1answer
50 views

Temperature increase during friction

There is pin made of Asbestos and two disc material Aluminum and steel in first experiment i used Aluminum disc with asbestos pin in wear test the disc is rotating and the asbestos was in frictional ...
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1answer
37 views

The different in wear test when using Aluminum and Steel disc in pin on disc apparatus

In wear test of pin on disc apparatus i found that mass loss of pin when i used Aluminum disc is higher than when i used Steel disc under the same conditions ,pressure, velocity and contact time can ...
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1answer
91 views

Is the MaxEnt “interpretation” of statistical mechanics the current mainstream approach?

I've only recently started studying statistical mechanics and I'm quite confused with the MaxEnt and anti-MaxEnt ideas. I'm looking for a concise answer, if it is possible, not really a description ...
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45 views

Difficulty in understanding Maxwell Boltzmann distribution in case on ions in a field

I learned that the velocity of molecules obey Maxwell Boltzmann (MB) distribution at a Temperature T. If I have ions of mass 'M' accelerated to 2eV in a specific region. As the ions are not ...
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1answer
73 views

Expected value of an operator in the microcanonical ensemble

I am following professor David Tong's lecture notes on Statistical Mechanics and on page 9 of this file http://www.damtp.cam.ac.uk/user/tong/statphys/one.pdf he states that the expected value of an ...
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32 views

What is the relation between scattering amplitudes, fluctuations, response functions and correlations in macroscopic equilibrium systems?

In Kardar's book Statistical Physics of Fields, he mentions that that correlations at different length scales can be measured by scattering. If its electric correlations, you would scatter light and ...