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

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38 views

2 D random walk first return to origin [on hold]

If I have a 2d random walk starting from origin, the probability distribution of return to the origin is n/(log n) after n steps. What is the probability distribution of 'first' return to the origin ...
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35 views

Why is a random walk's RMS distance from the starting position$\propto\sqrt{N}$? [on hold]

Why is the root mean squared (RMS) distance from the starting position of a (1D, 2D, or 3D) random walk of $N$ equally-sized steps proportional to $\sqrt{N}$? Is it also$\propto\sqrt{N}$ for ...
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1answer
24 views

Helmholtz energy in terms of grand partition function

According to my source of notes $$A = kT \left ( N \ln z-\ln Z(z, V, T)\right) $$ where $z=e^{\beta \mu}$, $\mu$ being chemical potential, $Z(z,V,T)$ is partition function for grand canonical ...
1
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31 views

The Ideal Gas Equation in higher dimensions

Basically I wanted to know whether or not the ideal gas equation, $PV=NkT$ would hold in higher dimensions? If so, how would you go about proving this? I can't see any reason as to why it shouldn't ...
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1answer
13 views

Example of a system where we cant measure the total possible microstates of a system but can measure the microstates of most probable state?

I have been reading about entropy and I read that entropy is basically a measure of total possible microstates but there was an approximation that when no. of particles become very large we take ...
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1answer
25 views

What does ''population'' mean in regards to the excited and ground states of an atom?

I have a problem I'm working on. It seems simple enough, but there is a term I'm not familiar with. It asks for the ''relative populations of the first excited and the ground states for helium gas in ...
2
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14 views

Nose-Hoover Barostat

Much can be found about the Nose-Hoover Thermostat. However I seem to be having difficulty finding out details about the Nose-Hoover Barostat, and how it is implemented. Would anyone be able to give ...
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29 views

Maxwell-Boltzmann distribution in Lennard Jones units

I'm studying thermostats in Molecular Dynamics. A very easy way (and poor, but I don't care for the moment) to implement a thermostat is to randomize momenta at some steps. These new momenta are ...
3
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48 views

Physical interpretation of the chemical potential in Bose and Fermionic gas

I understand that both Fermions and bosons have the chemical potential $\nu <0$ when it is T>0, but still behave classically, the fermions would increase its chemical potential at T=0, whereas the ...
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27 views

Classical Quantum or Relativistic?

An ensemble contains free electrons at 10^3 electrons per m^3 at 10^7 K. What can this ensemble be treated as: a Classical Quantum or Relativistic gas or in some overlapping domain?
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1answer
53 views

How does the fundamental assumption of statistical physics make sense?

Consider two systems A and B in thermal contact. System A has $N_A=3$ simple harmonic oscillators and the system B has $N_B=3$ simple harmonic oscillators as well. Each system has a number of energy ...
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34 views

Free energy in magnetic materials [on hold]

The phenomenological description of magnetoelectrics and multiferroics is based on the series expansion of the free energy is powers of the magnetic and electric fields. WHY IS IT EXPRESSED IN TERMS ...
2
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1answer
76 views

Gibbs entropy, Clausius' entropy and irreversibility

I have a bunch of doubts and confusions on the concept of entropy which have been bothering me for a while now. The most important ones are of a more technical nature, arisen from the reading of this ...
0
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1answer
21 views

Can collisions between particles in the canoncial ensemble be represented by a potential?

The professor in a statistical mechanics class said that in the canonical ensemble, you could represent interaction between particles as a potential in the partition function expression. But how about ...
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18 views

Understanding the concept of temperature vs. mean energy/heat capacity of a system

I need help understanding a concept in thermodynamics. What is the relationship between temperature and mean energy? What is the relationship between temperature and heat capacity? What I know: ...
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1answer
64 views

Does fluctuation really occur in equilibrium as its microstates are allowed to occur by Fundamental Postulate in equilibrium?

The Fundamental Postulate says: In equilibrium, all accessible microstates are equally likely. Accessible means having same energy.(right?) Let a container is taken full of gas having number of ...
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12 views

Forward and backward work distributions in fluctuation theorem

Fluctuation theorems such as Jarzynski equality and Crooks theorem (Link), show that $\frac{P_f(W)}{P_b(-W)}=\,exp[\beta(W- \,\Delta F)]$ where $W$ is work done on the system during each ...
5
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1answer
78 views

Why do we work in thermodynamic limit in statistical physics?

It is often stated that we work in thermodynamic limit at the beginning of courses on statistical physics $$N \to \infty, V \to \infty, \quad\frac{N}{V}=n=\textrm {constant}$$ what is less often ...
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20 views

Does ergodic hypothesis depend on the volume constraint of the macrostate or it only concerns with the energy constraint of the macrostate?

Ergodic hypothesis says that: [...] ergodic hypothesis says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the same energy is ...
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1answer
141 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 ...
2
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2answers
62 views

Microstates, Distribution of Particles, and the Probability of an Empty Compartment

If I have a closed system composed of $N$ particles and $p$ compartments, the total number of microstates available to that system is $$ p^N $$ Now say I want to find the probability that any one of ...
3
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1answer
103 views

Number theoretic loophole allows alternative definition of entropy?

A bit about the post I apologize for the title. I know it sounds crazy but I could not think of an alternative one which was relevant. I know this is "wild idea" but please read the entire post. ...
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2answers
97 views

Why is entropy defined as a discrete sum over all microstates in classical case?

I'm reading about statistical definition of entropy, which says $$S=-k_B\sum_ip_i\ln p_i,\tag1$$ where $k_B$ is Boltzmann's constant, and $p_i$ is probability of $i$th state to be occupied. But in ...
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2answers
100 views

Doesn't the success of statistical physics seem somewhat unreasonable?

It seems to me a rather big coincidence that statistical physics works so well. I can see how consistent macroscopic observations can occur just because the microstates that give rise to that ...
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31 views

Have we found a resolution to the Loschmidt paradox? [duplicate]

Loschmidt's Paradox (also known as the Reversibility Paradox) claims that it is not possible to deduce an irreversible process from time-symmetric dynamics such as the classic dynamics. This puts the ...
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1answer
31 views

Partion function for ideal gas - why use only one octant?

In these lecture notes (page 2) and in other sources I have checked, it says that the number of states with $k\in[k,k+dk]$ is: $$dN=\frac{4\pi k^2V}{8\pi^3}$$ Saying the factor of $8$ comes from the ...
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14 views

Monte Carlo Metropolis method - trial step algorithm [migrated]

I'm working on a Magnetization simulation and writing an algorithm using the metropolis method. I am using a change in energy and a Boltzmann distribution, but, my question is about the trial step. ...
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1answer
35 views

Reference for statistical mechanics from information theoretic view

I am interested in knowing if some one here knows book/notes for statistical mechanics from the information theoretic viewpoint.
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1answer
45 views

Relation between the $N$ particle partition function and probability?

For the 1 particle partition function the probability that the particle is in the state with energy $\varepsilon_i$ is given by: $$P_i =\frac{e^{-\varepsilon_i \beta}}{Z_1}$$ where $Z_2$ is the 1 ...
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30 views

Books on Introductory Statistical Mechanics

Can anyone recommend a good book on Basic Statistical Mechanics? I have an engineering background and had to go through loads of different books to learn General Relativity. I found Peter Collier's A ...
2
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20 views

Non-equilibrium electronic distribution in the time-relaxation approximation - Which is the boundary condition?

In Chapter 13 of Ashcroft-Mermin - "Solid State Physics", the following non equilibrium electronic phase-space distribution for the semiclassical electrons in a periodic crystal is derived: ...
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38 views

Does it take the same amount of time, it takes for a system to get to a low-entropy (fluctuation) state from equilibrium, to go in the other way?

Let a system be in a state of fluctuation - a state of low-entropy at $t_0\;.$ Then before and after a sufficiently large but finite time-interval, the system would again be at equilibrium. As the ...
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22 views

Fugacity in Bose-Einstein condensate

Just a simple question, I didn't manage to find out in my books... The fugacity $z = e^{\beta \mu}$ in the case we have condensation in a bose statistics. Is it always 1 or $z \to 1$? In the ...
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30 views

free energy in the path integral equivalent to the classical 1D Ising model: Shankar

In chapter 21 (eqtn 21.2.90) Shankar gives the free energy (of the PI problem equivalent to the classical 1D Ising model), $$ f=-E_0 = K^* $$ I dont understand how he arrives at this considering in ...
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1answer
48 views

Kinetic theory of physics [closed]

$$E = (3/2) kT$$ For average kinetic energy of a molecule gas.The constant $k$ does not depend on the type of molecule. Can this result be true for both hydrogen and chlorine?
3
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1answer
86 views

Thermodynamic free energy

The thermodynamic free energy is defined by $F=U-TS$ with $U,T,S$ being the internal energy, temperature and entropy respectively. I have also seen another formula for the free energy, $F=-T \log{Z}$ ...
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23 views

Radiation collapse to black hole

I want to find the temperature at which radiation in AdS will collapse to form a black hole. I have even found a reference that gives the answer but I cannot understand it: ...
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0answers
47 views

inverse problem for specific heat of fermion .. has been solved?

hi given the specific heat is given by an integral equation $$ C(T)=\int_{0}^{\infty}d\nu g(\nu)\frac{u^{2}}{(e^{u\nu}+1)^{2}}\nu^{2}$$ where $ u= \frac{h}{kT}$ my question is is the following ...
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24 views

Reference request: 2D conformal field theory and functions on the triangular lattice

I don't have much of a physics background and was wondering if anyone knows what is meant by "conformally invariant" functions defined on the plaquettes of the honeycomb lattice (ie functions defined ...
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29 views

Volume Operator / volume phase-space-function in thermodynamics

In Thermodynamics, one often encounters the derivation of pressure as the generalised force that belongs to the extensive state-variable of the volume. Postulates: One looks just at a system of many ...
5
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1answer
55 views

Cluster Expansion

In the cluster expansion (section 5.2 in M. Kardar "Statistical Physics of Particles") we write the grand canonical partition function. During the expansion, we do the following switch between a sum ...
1
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1answer
31 views

thermodynamic generalized force and thermodynamic potential

I have stumbled across these and have taken some interest. Are the meanings of generalized "force" and "potential" the analogous to the case of mechanics where the derivative of one with respect to a ...
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3answers
63 views

Correlation function $\langle s_1(x, t)s_2(x', t')\rangle$ vs $\langle s_1(x, t)s_2(x', t')\rangle-\langle s_1(x, t)\rangle\langle s_2(x', t')\rangle$

The correlation function in statistical mechanics is defined in either of two ways $$g(\mathbf{x}-\mathbf{x}', t-t') = \left\langle s_1(\mathbf{x}, t)s_2(\mathbf{x}', t') \right\rangle$$ ...
0
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1answer
48 views

CFT and temperature

I have tried to think about this for some time but could not really go anywhere. Sorry for the sloppy question and thanks for any pointer. My question is about CFT at finite temperature and ...
7
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2answers
126 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 = ...
0
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1answer
32 views

Proving the existence of temperature from zeroth law in the MIT OCW notes

This question refers to the following set of lecture notes: ...
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138 views

Why does warm water sink?

It is well known that water at 4C is denser than water at 0C. This is the usual explanation for why a body of water freezes from the surface (also it's because ice is even less dense, but that's ...
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2answers
93 views

Why can't the entropy of an isolated system decrease? [duplicate]

I read that heat cannot flow from cooler body to hotter because for that entropy of the system becomes negative. Why is that so? Why we cannot have negative entropy?
2
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1answer
47 views

Why do randomly flying gas molecules have a distribution of energies?

Why do randomly flying gas molecules have a distribution of energies? This is a question from my chemistry textbook (not homework, just questions to help us think about and understand the concepts). ...
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18 views

Eigenvalues for correlation matrix which have the form of an harmonic function

I am trying to understand the written in the picture below. I took the matrix $C_{2 \times 2}$ which is: $$C=\left[ \begin{array}{} a& ace^{-\frac{|\phi_1-\phi_2|}{2}}\\ ...