# Tagged Questions

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

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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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?
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### 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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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### 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 $$g(\mathbf{x}-\mathbf{x}', t-t') = \left\langle s_1(\mathbf{x}, t)s_2(\mathbf{x}', t') \right\rangle$$ ...
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### 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 ...
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### The energy density of states for a 2D electron gas [closed]

I am currently trying to solve for the electron density of states of an electron gas system restricted in 2D. I managed to find f(k)dk, the density of states with respect to the wave vector and i know ...