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

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Sticky physics of pasta mixture [duplicate]

When you mix cooked noodles or other "prevailing 1D pasta" like spaghetti with other ingredients like olives, pieces of meat (not minced) etc. you will probably experience the fact, that the mixture ...
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1answer
74 views

How to determine rotational energy of gas molecules

For an arbitrary polyatomic molecular gas, what is the expected behavior of $U_{rot}(T)$, the rotational kinetic energy of the atoms, in the two limits T high and T low? So far, I have written an ...
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97 views

Time between two collisions in a 2D gas

I'm trying to code a simulation of a 2D gas in a box. The molecules are represented by circles of radius $R$ having elastic collisions with the walls only (for now). I read that the average time step ...
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1answer
165 views

Can entropy be regarded as energy dispersal?

In several answers here the claim has been made that thermodynamic entropy can be regarded as energy dispersion. See, in particular here, and here and here. This is apparently the pet theory of a ...
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1answer
103 views

Monte Carlo with zero-temperature: trapped in a local minimum

I have a problem reaching the correct ground state while performing a Monte Carlo at zero temperature. Some parts of the system get trapped in a local minimum, and for getting the global one (the ...
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2answers
82 views

how to simulate a steep potential barrier in langevin equation

When simulating a Langevin equation, how is a vertical potential barrier handled? I have the time overdamped evolution of the position $x$, described by $\gamma\frac{dx}{dt}=-V'(x)+\eta(t)$ where $...
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1answer
59 views

Temperature of system in canonical ensemble

Upon reading Reif's explanations relating to systems exchanging energy and the canonical ensemble (Reif, Fundamentals of statistical and thermal physics, p. 95ff and p. 202ff), I am led to conclude ...
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84 views

On the surface, is the law of maximum entropy production the same as principle of least action?

I just have read about the law of maximum entropy production. Someone has idolized it enough to make an whole website just for it: http://www.lawofmaximumentropyproduction.com/ A system will ...
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1answer
66 views

Probability in canonical ensemble - relation to temperature

I've got a conceptual question about the canonical ensemble. In the derivation of the probability distribution (see e.g. Kardar, Statistical physics of particles, p. 110ff) it is stated that a small ...
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36 views

Is the wavefunction of particles inside a gas spread or localized?

For an individual free particle that starts localized, the wave function packet spreads over time, so the particle becomes less localized. Suppose now that we have a gas of those particles inside a ...
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1answer
70 views

Which quasiparticles follow which statistics [closed]

Let me say beforehand that I know this is an ill-defined question, but I believe it is useful anyway. For these common quasiparticles: Phonons Holes Plasmons Excitons Plasmon-polaritons What ...
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5answers
171 views

Does gravity acting on a resting object produce any heat?

Let's compare two systems. System 1: A box is completely isolated. There are no forces acting on that object, and no interactions of any kind with other objects, waves, etc.. System 2: The same box ...
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4answers
208 views

What is the cause for the inclusion of 'thermal equilibrium' in the statement of Ergodic hypothesis?

This is the fundamental assumption of statistical mechanics: In an isolated system in thermal equilibrium $^1$, all accessible microstates are equally probable. But why does it mention the ...
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1answer
35 views

Does nucleation depend on the rate of change in pressure in a carbonated liquid?

Carbonated beer flowing from a keg through a short length of tubing results in large quantities of foam. Unintuitively (at least to me), increasing the length of tubing results in a less frothy drink. ...
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14 views

What is the motivation behind defining short range order the way it is defined in Braggs-William approximation?

I am reading Statistical Mechanics by Kerson Huang. In the chapter on Ising model, it defines short range order as $\frac{2 N^{++}}{\gamma N}$ where $N^{++}$ is total number of spin up neighbours of ...
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1answer
66 views

Speed of spontaneous mixing of different gases

Suppose we have a rectangular box divided into two equal cubic parts by a vertical impenetrable wall. Part 1 of the box contains a standard state mixture of $(1-x)$ mole of gas $A$ (e.g. Oxygen) and $...
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25 views

conduction band and free electrons the properties of electrons in conduction band

Do electrons in conduction band consider as free electrons? or they are not completely free? so that we can calculate the distribution function and the density if states ??
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130 views

Change in statistical Entropy negative?

I'm currently stuck with a particular problem: The total energy of a set of molecules in an "isolated" container does not change when the container volume expands by a factor of 2, ...
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1answer
75 views

Heuristics behind Dirac delta function in Master equation for probability?

I'm reading this paper [Phys. Rev. Lett. 106, 160601 (2011)] and it studies simple diffusion where a particle stochastically resets to its initial position $x_0$ at a constant rate $r$. As you can see,...
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2answers
264 views

What is the correct relativistic distribution function?

General Statement and Questions I am trying to figure out the proper way to model a velocity/momentum distribution function that is correct in the relativistic limit. I would like to determine/know ...
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2answers
70 views

temperature from a molecular point of view

The electric fan increases the velocity and hence the kinetic energy of the molecules in the air. this would mean that the temperature has increased. What's wrong with a conclusion? I want you to ...
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1answer
77 views

Does the canonical partition function count microstates?

The microcanonical partition function is the density of states. The canonical one, from a dimensional point of view, is still a number of states, but does it actually count microstates? I tried ...
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16 views

Role of Chemical potential in Bosonic gas

How does the chemical potential allow us to distinguish different quantum gas, in particular why is it true that for bosonic gas always have chemical potential smaller than or equal to 0.
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2answers
138 views

Derivation of ideal gas law

I looked up on the ideal gas law which our high school textbook derives with the empirical Combined Gas Law. However, the textbook did give a good explanation for this equation $$pV = \frac{N}{3}m\bar{...
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2answers
71 views

A small issue in renormalisation group formalism

In the general RG formalism, suppose $\vec{\mu}$ represents a vector in parameter space and $\vec{\mu}^*$ is the fixed point under the transformation $R$. Then for $\vec{\mu}=\vec{\mu}^*+\delta \vec{\...
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56 views

Proof of periodicity of Floquet Green's function

It is claimed in many papers that the two-time Green's function in time periodic Hamiltonian case is periodic in the average time, i.e. \begin{equation} G(t+T,t'+T)=G(t,t') \end{equation} when $H(t+...
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11 views

Particle damping at low pressures

I'm looking for references on the topic of particle damping at low pressures, where the interactions are rare enough so that collisions are discrete, and the effective damping has to be integrated in ...
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2answers
382 views

Bose-Einstein condensation and phase transition

I would like to ask the following question for which I cannot find a definite answer in the literature. Of what ORDER is the phase transition leading to Bose-Einstein condensation for a ideal and ...
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1answer
114 views

Partition Function and BlackBody Radiation

I'll start with a few definitions: $$\beta \equiv \frac{1}{k_bT}$$ Where T is the temperature of a system. And the partition function: $$Z \equiv \sum_{j}e^{-\beta \epsilon_j}=\int D(\epsilon)d\...
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74 views

${\phi}^4$ description of Ising ferromagnet

Suppose the coupling between two spins is $C_{i,j}<0$, then the classical partition function is given by $$Z=\sum_{\{s_i\}}e^{\sum_{i,j}s_iK_{ij}s_j+h\sum_{i}s_i}$$ where $K_{ij}=-\beta C_{ij}$ and ...
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21 views

Role of density of states of electrons in a solid

When studying the statistical mechanics of a solid such as a conductor or a semi-conductor, does the density of states of electrons play a role in the calculation of the heat capacities? I know that ...
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1answer
33 views

Can dynamic considerations apply to the statistical mechanics?

I'm learning statistic mechanics this semester, but some intuitive questions haunted me all the time. First, according to the Ergodic Theorem, all states of a system is equally possible. Let's ...
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40 views

Thermodynamics for 1D line of 3D dipoles

The 1D Ising model was solved almost a century ago. This model assumed spins that point along the 1D line to the left or right and only considered nearest neighbors, so that the Hamiltonian with no ...
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1answer
111 views

Derive the Boltzmann factor in classical statistical mechanics

In both quantum and classical statistical mechanics, the probability of an NVT system having an energy $E$ is proportional to $$ p(E)\propto e^{-E/T} $$ However, all of the derivations (that I can ...
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3answers
325 views

Seemingly a paradox on the eigenstate thermalization hypothesis (ETH)

In the research field of Many-body Localization (MBL), people are always talking about the eigenstate thermalization hypothesis (ETH). ETH asserts that for a isolated quantum system, all many-body ...
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1answer
418 views

Why liquids and solids are mostly regarded as incompressible?

In many continuum-mechanical Problems it is assumed that liquid and solid substances cannot Change the total value of volume where it holds $\rho = const, \vec{\nabla}\cdot \vec{v} = 0$. In the 1-...
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27 views

Question about the derivation of Linearized Boltzmann equation

I'm following the textbook Statistical Mechanics of Schwabl. He introduces a small pertubation to the global Maxwell distribution $f_0(v)$ by $f(x,v,t)=f_0(v)\left(1+\frac{\nu(x,v,t)}{kT}\right)$. ...
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64 views

Thermodynamic expectation value at $T=0$

The thermodynamic expectation value for an observable $A$ is defined as $$\langle A \rangle = \frac{1}{Z} \sum_n \langle\psi_n| e^{-\beta H} A|\psi_n \rangle, \qquad (1)$$ where $\beta=1/k_bT$, the $\...
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35 views

Phase space Distribution

According to equal a priori principle, the probability of find a system in any of its micro state is equal. But when we take an ensemble of system, we define a probability distribution function. How ...
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1answer
205 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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74 views

Spatial correlation function and translation invariant

recently, i was puzzled by the spatial correlation function. in textbooks of statistical physics, they say that if the system is translational invariant, then the spatial correlation function f(x1,x2)=...
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1answer
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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0answers
171 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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221 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. 4.6....
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19 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
31 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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1answer
55 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 http://www.sklogwiki.org/SklogWiki/...
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30 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
41 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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69 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 ...