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

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2answers
1k views

Physics-based derivation of the formula for entropy

I am looking for a derivation of the formula $$S~=~-\Sigma_ip_i \log (p_i).$$ for entropy, from first principles. I only wish to assume the laws of physics, and without involving concepts in ...
1
vote
1answer
105 views

Spontaneity / Free Energy of Non-Isothermal Process

I'm trying to determine a lower bound for the work input necessary to make an entropy-reducing process "spontaneous" in the sense that the 2nd law is not violated. For a constant temperature and ...
1
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0answers
18 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 ...
0
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0answers
30 views

definition of Hamiltonian in statistics [on hold]

Is there any advantage to use $\hat H-\mu \hat N$ instead of $\hat H$ as the hamiltonian in statistical mechanics?
2
votes
0answers
36 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 ...
1
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1answer
257 views

Virial theorem and the energy in a gas

I clearly am interpreting the Virial Theorem incorrectly, but I don't know how. In dipole gases, the molecules can exhibit five kinetic modes, while they can only experience 2 potential modes. Doesn't ...
3
votes
2answers
103 views

what does “an average over noise” mean in Zwanzig's book

This is a very specific question about Robert Zwanzig's book Nonequilibrium Statistical Mechanics. Specifically, what is he talking about in equation 1.25 on page 10 that he calls "an average over ...
0
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1answer
27 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 ...
3
votes
1answer
130 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 ...
2
votes
3answers
808 views

Question about the proof that heat capacity goes to zero if temperature approaches $0K$

I don't completely understand the proof that is given for the claim that the heat capacity goes to zero, if the temperature approaches $0K$. They do it as follows, if $C_x$ is the heat capacity where ...
-2
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0answers
26 views

Finding root mean square speed of an ideal gas [on hold]

Again a question ive never seen in my life... The molecules of an ideal gas have a root mean square speed of 520 meters per second at a temperature of 27 degrees celcius. Calculate the r.m.s speed ...
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votes
1answer
88 views

Why is not the entropy of earth increasing? [on hold]

The entropy of earth is not increasing significantly in the past billions of years. So what is the reason? It must be because of the sunshine. But I still do not have a concrete picture.
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0answers
26 views

Simple mean-field “lattice gas” model [on hold]

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 ...
2
votes
1answer
239 views

Local minima in Ising model in a Monte Carlo simulation

Is there any way to check whether in a Monte Carlo simulation using Ising model is stuck in any (false) local minima of energy or not, particularly in 3D system ?
2
votes
1answer
175 views

Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
2
votes
0answers
50 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.
1
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0answers
29 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 ...
1
vote
1answer
436 views

phase-space volumes or cells for N particle system

For $N$ non interacting spinless particles in a volume, we have $3N$ degrees of freedom and we can divide the phase space into $6N$ dimensional cells of volume $h^{3N}$. Each cell represents a state ...
2
votes
1answer
147 views

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 ...
0
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0answers
23 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) = ...
0
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2answers
418 views

How does temperature relate to the kinetic energy of molecules?

In ideal gas model, temperature is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly ...
0
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0answers
18 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 ...
1
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1answer
41 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. ...
4
votes
1answer
228 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 ...
1
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1answer
80 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
votes
2answers
370 views

Black hole entropy

Bekenstein and Hawking derived the expression for black hole entropy as, $$ S_{BH}={c^3 A\over 4 G \hbar}. $$ We know from the hindsight that entropy has statistical interpretation. It is a measure ...
4
votes
2answers
137 views

Where and how is the entropy of a black hole stored?

Where and how is the entropy of a black hole stored? Is it around the horizon? Most of the entanglement entropy across the event horizon lies within Planck distances of it and are short lived. Is ...
0
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0answers
15 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 ...
2
votes
1answer
42 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 ...
8
votes
3answers
746 views

Why must the particles of an ideal gas be point-like?

Why is a gas of elastically colliding hard balls of finite size not ideal? Respectively: Why is it essential that the particles of an ideal gas are point-like? Especially: Which ...
5
votes
2answers
442 views

Renormalization Group and Ising with d=1 and D=1

I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations $K'(K)$, $q(K')$ $K(K')$, $q(K)$ between the coupling costants. My problem arise ...
4
votes
2answers
199 views

Counting Problems in Physics

What are some classic counting problems in physics? I'm trying to think of interesting examples to give in a math class on the matter, and I feel as if physics should have some ones to offer.
0
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1answer
27 views

Thermodynamic transformation

Why it is so that any reversible thermodynamic transformation is quasi- static ? Also, Why the converge is not necessarily true ?
0
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1answer
30 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 = ...
0
votes
1answer
28 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 ...
3
votes
1answer
191 views

H-theorem and Boltzmann equation applied to Boltzmann distribution

Using the Boltzmann equation: $$ \frac{dH}{dt} = \int_0^{\infty} dr \int_0^{\infty} ds W(r,s)[p_r - p_s][\ln{p_r} - \ln{p_s}],$$ and assuming $p_r = e^{-\beta r}$, the equation looks like $$ ...
8
votes
8answers
1k views

Entropy increase vs Conservation of information (QM)

Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of ...
2
votes
0answers
49 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? ...
0
votes
1answer
21 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 ...
5
votes
2answers
142 views

Simple estimation of the critical temperature of water

I'm trying to develop fermi estimation skills and I came up with a question for which I don't even know where to start from. Here goes: Is it possible to estimate the critical temperature (say in ...
0
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1answer
184 views

What does the behavior of the pair correlation function look like in the vicinity of the critical point?

What does the g(r) look like near the critical point? I know what the pair correlation function (radial distribution function) should look like for a solid, which has regular packing and therefore ...
2
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0answers
45 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 ...
0
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2answers
24 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 ...
0
votes
1answer
40 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 ...
-1
votes
1answer
67 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 ...
18
votes
1answer
238 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each ...
2
votes
1answer
66 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?
4
votes
2answers
136 views

What materials are used in non thermal plasma?

While reading about non-thermal plasmas, I came across their ionization potentials(~1%), and other capabilities, such as their non Maxwellian energy distributions. At what temperatures, and pressures ...
5
votes
1answer
101 views

Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...
15
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1answer
1k views

Motivation for the use of Tsallis entropy

Every now and again I hear something about Tsallis entropy, $$ S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1} $$ and I decided to finally get around to investigating it. I haven't ...