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

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about Conservation laws and Correlation function

I'm reading a review paper by Gorden Baym-(http://www.worldscientific.com/doi/abs/10.1142/9789812793812_0002) In the second part, he raised that: According to conservation law $\frac{\partial ...
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1answer
58 views

Fermi energy on a “fermion pre-gas model”

I'm having serious trouble while trying to follow an example from Callen's "Thermodynamics and an introduction to Thermostatistics" regarding the definition of the Fermi energy. In said example one ...
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1answer
87 views

Why is the correlation of an observable and its derivative zero?

Why is the correlation of an observable and it's derivative zero? And why does this not only hold for $\langle A(t) \dot A(t) \rangle $ but also for $\langle A(0) \dot A(t) \rangle $ ? These averages ...
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2answers
212 views

Multiplicity vs Partition function

I'm a little confused between all the different notations for the multiplicity and partition function. They're not the same thing, are they? I know that entropy can be expressed as $ S = k \ln\Omega ...
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1answer
32 views

Adjoint Fokker-Plank operator

In Zwanzig's book "nonequilibrium statistical mechanics" he defines the Fokker-Plank equation for a probability distribution $f$ and with it an operator $D$: $${ \partial f(a,t) \over \partial t} = ...
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3answers
96 views

Does the ratio of thermal energy to planck's constant have physical significance?

I realized that I had never noticed that $\left[ \frac{\hbar}{k_B T} \right]=$ Time. At $T \approx 300 K$, we have $\frac{\hbar}{k_B T} \approx 10$ fs. What, if anything, does this quantity mean? Does ...
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49 views

Wick's theorem: Classical Version. Derivation question and what happens with odd moments? [closed]

I am trying to prove the classical version of Wick's theorem: For a set of random variables ${a_i}$, with covariance matrix $M$ and $\rho(\vec a)$ a Gaussian probabilitiy density: $$\langle a_j a_k ...
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1answer
156 views

What is the physical fundamentals of Pascal's law

Pascal's law or the principle of transmission of fluid-pressure (also Pascal's Principle) is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible ...
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1answer
148 views

Critical temperature and lattice size with the Wolff algorithm for 2d Ising model

When I run my implementation of the Wolff algorithm on the square Ising model at the theoretical critical temperature I get subcritical behaviour. The lattice primarily just oscillates between mostly ...
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1answer
51 views

What's the difference between the Fermi level and the electrochemical potential?

I was asked in a Thermostatistics test to compute the electrochemical potential $\mu(T)$ and the Fermi level $\epsilon_F$ for a system of non-interacting fermions, with two possible energetic states ...
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1answer
47 views

Why classical open system and Bose-Einstein condensate are not fundamentally the same?

The classical partition function for an open system is given as $$ Z_{\text{max}} = \sum_{N=0}^{\infty} \dfrac{h^{-N}}{N! } \prod_{j=1}^{N} \left( \sum_{i=0}^{\infty} e^{-\beta (E_{ij}-\mu)} g_{i} ...
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35 views

What does the particle to volume density physically mean for Bose-Eisenstein condensate?

The average number of particles $\langle N\rangle$ for a Bose-Eisenstein condensate in 3D is given as $$ \dfrac{\langle N\rangle}{V} = \dfrac{V^{-1}}{e^{\beta (0-\mu)}-1} + \int_{0}^{\infty} ...
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1answer
75 views

Good book for learning fluid statistics

I'm currently using Gray and Gubbins Theory of Molecular Fluids to learn about the statistical physics of fluids. It may be a fine reference text, but I'm not impressed with it as an introduction to ...
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1answer
626 views

Simpler derivation of Sackur-Tetrode equation

Is there a reason the following derivation for the Sackur-Tetrode equation is not common? I am teaching a lower undergraduate level class and would like to derive it with simpler terms of only using ...
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2answers
117 views

What are the definitions of microstates and macrostates?

I have been looking up definitions for microstates and macrostates of a thermodynamic-system. I am looking for clear conditions for systems to be in the same macro- or microstate, but have had no ...
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1answer
75 views

Order parameter in Landau's theory for second order phase transition

Above is a screenshot of Kadanoff's review article "more is the same". The free energy in Landau's theory is very well known, but the highlighted sentence seems to be quite confusing. First of all, ...
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1answer
39 views

How photons get distributed in a system?

Let's say I'm in a room, and there are plenty of things in my room like carpet,mirrors,glass and other stuff.And I see there are shadow regions and fully bright regions, and I want to know how photons ...
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0answers
36 views

Relaxation time approximation in anisotropic potential scattering event

In relaxation time approximation (RTA) of Boltzmann transport theory, the relaxation time is calculated by $\frac{1}{\tau(\mathbf{k})}=\frac{2 \pi}{\hbar V}\sum_{\mathbf{k^{'}}} \delta ...
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1answer
343 views

Calculate pressure from partition function with separated volume geometric parameters?

How does one calculate the pressure from the partition function if it is specified in terms of three parameters defining the space of which the gas occupies, but all three parameters are not always ...
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1answer
133 views

Why does Landau theory not fail when dealing with a first order phase transition?

Here is a problem where I can do the calculation, but I am not understanding the philosophy behind it. It is about Landau theory: The Landau theory of phase transitions is based on the idea that the ...
3
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3answers
638 views

What is the physical meaning of the Lindblad operator?

I read the wikipedia article on the Lindblad operator, but I still don't understand what this operator is supposed to describe. I therefore considered setting up an example in order to get the idea. ...
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1answer
246 views

Is average kinetic energy equal to the total thermal energy of a gas?

"Average KE" as in this equation: $$K_{average} = \frac{3}{2} kT$$ Since potential energy in ideal gas model is eliminated, I guess this equation is also for the total thermal energy of a gas/a ...
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109 views

Exact expression for the coefficient in Bloch-Grüneisen (BG) formula?

In most representations of the BG formula, there is a coefficient (usually left vague as an experimental parameter, but sometimes written out "analytically") in front of the integral: $$\rho=\rho_0 +A ...
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1answer
119 views

Drag force acting on a disk in a 2D system

I have a 2-dimensional system with behavior governed by Langevin dynamics in which disks (circles) move through a fluid. In the Langevin equation, there is a velocity-dependent term that accounts for ...
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1answer
78 views

Why is Fermi-Dirac type of distribution used in semiconductors?

We assume that distribution of electrons follows Fermi-Dirac distribution / statistics in semiconductor model which will help to find the concentrations of electron and holes and the relationship ...
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0answers
47 views

Simple mean-field “lattice gas” model [closed]

I'm having some conceptual problems with a simple mean-field "lattice gas" model and I'd be glad if someone could help me go further. Basically the model consists of the following hamiltonian: $$ H ...
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0answers
41 views

A functional average calculation confusion within Gaussian planar model's RG

I am trying to follow some detailed calculation in a famous paper [John, B. Kogut, Rev. Mod. Phys. 51, 659 (1979), An introduction to lattice gauge theory and spin systems]. More precisely, please ...
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0answers
44 views

bose einstein phase transition

From Carter's book Thermodynamics and Statistical Mechanics, the partition function of a bose-einstein gas in $d$ dimensions is $$ \ln(Z) = ...
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0answers
36 views

Making Pudding; A complicated non-equilibrium statistical process?

There are a lot of non-equilibrium processes examples given in physics literature. But some processes that are present in everyday life are not treated. As an example, the formation of pudding can be ...
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1answer
144 views

Conformal blocks in 2D CFTs

I have studied conformal field theories in two dimensions and I understand the basic idea behind conformal blocks too. But I never completely realized what they are when it comes to computing them. ...
2
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0answers
73 views

Topological order and entanglement in quantum quench problem

I would like to ask about useful reviews, must-read papers on the study of topological order and entanglement in quantum quench problems that give a good introduction to the topic.
2
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1answer
47 views

Ewald summation without repeating one particle periodically?

I need to perform an Ewald summation for a Brownian Dynamics simulation. In the normal Ewald summation procedure, all particles in the simulation box are periodically repeated in the neighbouring ...
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1answer
102 views

canonical ensemble that is quantum mechanical and continuous?

I do not understand what the following statements from Wikipedia mean For a canonical ensemble that is quantum mechanical and continuous, the canonical partition function is defined as $$ Z = ...
2
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1answer
74 views

Are Fermi-Dirac-statistics relevant to view the universal system of neutrinos?

Should the energy distribution of neutrinos be affected by Fermi-Dirac statistics? And if so, what would the consequences be? Could this locally cause weak interaction because of the Pauli Exclusion ...
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1answer
39 views

Mono-atomic gas particles coupled by spring forces don't care how many particles are involved?

I calculated the partition function of $N$ classical atoms of identical mass $m$ who all experience a mutual spring forces with identical spring constant $k$. The Hamilton is \begin{align} H = ...
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1answer
151 views

How to explain the Venturi effect with Kinetic Theory?

From a macroscopic perspective a fluid flowing through a pipe gets accelerated when the pipe's cross section gets narrower. According to $F= ma$ a force must be present to do this. This force is ...
2
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0answers
58 views

Maximizing particle annihilation of a certain particle type?

Is there any theoretical situation where one would be able to maximize the production of a certain type of particle? I wish to continue discussing this question: Where would dark matter be produced? ...
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1answer
33 views

Can the energy/power required to mix two fluids together be calculated?

Given two fluids; say for example oxygen and nitrogen gases. By simply introducing, again for example 1 liter of each gas into a closed container, the process of diffusion alone will eventually cause ...
2
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0answers
74 views

Are temperature and chemical potential of a black hole independent quantities?

I am a bit confused about the independent parameters in a charged black hole in AdS spaces. From equation (63) of this lecture notes we see that the temperature (T) of the black hole has chemical ...
2
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0answers
74 views

Kinetic Theory of Liquids

I am familiar with the Kinetic Theory of a gas, where atoms or molecules are in relatively high-speed, random motion, and the bulk properties of the gas are determined by aggregations of these ...
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1answer
76 views

Entropy change in Heisenberg picture

If we stick with Heisenberg picture where density matrix $\rho$ is constant, how do we account for entropy increase? I've read the answer to State collapse in the Heisenberg picture but I don't see ...
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2answers
32 views

Dependence of heat absorbed on different ways of heating

Heat capacity depends on the delta Q (i.e small amount of heat absorbed) and delta T (i.e small change in temperature). My question is,why is the amount of heat absorbed different for different ways ...
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1answer
123 views

Thermodynamic transformation

Why it is so that any reversible thermodynamic transformation is quasi- static ? Also, Why the converge is not necessarily true ?
4
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1answer
248 views

What is the entropy of a mixed state in classical physics?

Consider a classical system which admits certain macroscopic level of description. It is known, that for two pure states $\omega_1$ and $\omega_2$ on this level of description the entropy of the ...
2
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1answer
99 views

Is the energy per degree of freedom $\frac{1}{2}kT$ in relativistic systems?

The equipartition theorem says that the mean energy per degree of freedom is $\frac{1}{2} kT$. Is this result relativistically correct?
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1answer
80 views

What are the distributions of electron speeds (a) in a star? (b) in a planet?

Ideally I would like to have an x-y graph of (x) speed relative to centre of mass of the body (star or planet) against (y) the number or percentage of electrons having that speed at a given moment in ...
5
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1answer
160 views

Hydrostatic forces in a bowl of cereal [duplicate]

This morning I was eating cereal which consisted of roughly spherical pieces just shy of one centimeter in diameter. By the time I was nearly finished, the cereal pieces were floating in a monolayer ...
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2answers
100 views

Partition function of a 3D vibrating string

Is the partition function of a 3D vibrating string a sum of discrete energies, an integral of an energy continuum, or both? $$ Z_{\text{disc}} = \sum_{k=1}^{\infty}g_ke^{-\beta E_k} $$ or $$ ...
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1answer
71 views

Momentum distribution function for a particle in a 1D box

In these notes on statistical thermodynamics (pp. 62), I encountered this [topic: particle in a 1D box]: We shall adopt the initial condition that the probability distribution function has the ...
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1answer
44 views

Find an expression for S(T,x) from tension and specific heat

I'm working on a problem from a Statistical Mechanics lecture series online, and on the homework, I hit a bump in this problem. Here is the problem set, and I'm asking about #1.c. Short version, we ...