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

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How are the charges on the plates of a capacitor distributed?

Given a specific overall amount of energy a rectangular parallel plate capacitor stores what number of atoms on a specific plate would have any given specific charge?
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1answer
19 views

The expression of the density in terms of molecular mass and the distribution function

I am reading a book about the boltzmann equation, the author gives the expression of the fluid density $\rho$ as follows: $$\rho(\mathbf r,t) = \int {M\,f(\mathbf r,\mathbf c,t) \, \mathrm d\mathbf c}$...
0
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21 views

How to derive entropy from density of states?

I'm trying to derive the entropy of a black hole, given the density of states of a bosonic string (the details are not relevant). The density of states is $$ \omega(E) = E^\alpha e^{\beta E} $$ The ...
4
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2answers
109 views

What is the black hole information paradox really? [on hold]

Preliminaries What is the black hole information paradox really? Is it a sophisticated way to ponder and debate the existence of an operator on the boundary that can tease out the interior of a ...
4
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3answers
433 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
1
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4answers
1k views

Must a reversible engine be a carnot engine?

I have this homework question: "Show that any reversible engine operating between T1 and T2 is a carnot engine." I think I have a solution, but it feels very hand-wavy. We know that any process that ...
0
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2answers
46 views

Relation between entropy and internal energy

I am confused as to what is the relation between entropy and internal energy. Entropy is always presented as a measure of the randomness in a system. So when we supply heat to a well insulated system ...
2
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1answer
187 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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0answers
32 views

Is there a block spin renormalization group scheme that preserves Kramers-Wannier duality?

Block spin renormalization group (RG) (or real space RG) is an approach to studying statistical mechanics models of spins on the lattice. In particular, I am interested in the 2D square lattice model ...
9
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2answers
256 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 = 4(\...
0
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1answer
46 views

What is the relationship between Maxwell-Boltzmann statistics, Boltzmann distribution and Maxwell-Boltzmann distribution? [on hold]

I have recently been studying some statistical thermodynamics and I am currently trying to understand all the different concepts of the course. I was wondering about differences between MB statistics, ...
10
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7answers
14k views

Recommendations for Statistical Mechanics book

I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly I just want it to be thorough and to include all the math. And of course,...
0
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17 views

Landau Diamagnetism and Pauli paramagnetism

In the conventional definition of Landau's diamagnetism we ignore the effect of spin-electron coupling and vice versa for the derivation of Pauli's paramagnetism. I want to know what would happen if ...
2
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0answers
20 views

Multi-Cut Matrix Models

I have a question pertaining specifically to a one-matrix model with a multi-cut solution. The standard procedure is to take a polynomial superpotential $W(x)$. In the classical limit (analogous to $...
4
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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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0answers
17 views

Video lectures for studying graduate level kinetic theory

As the title says it all, I require Video lectures for studying graduate level kinetic theory including but not limited to detailed analysis of viscosity and conductivity, diffusion and Maxwell's ...
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2answers
185 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 ...
15
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7answers
664 views

Relativity of temperature paradox

The imagined scenario: Part A: From special relativity we know that velocity is a relative physical quantity, that is, it is dependent on the frame of reference of choice. This means that kinetic ...
5
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2answers
57 views

Books on entropy [on hold]

What books introduce entropy in a intuitive, elementary way (at most, for a person with undergraduate physics studies)? The book should not necessarily introduce entropy in relation only to ...
1
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0answers
28 views

Specific heat of water

In statistical mechanics, we derive all the thermodynamic quantities, including specific heat $c_v$ from the partition function $Z = \mathrm{Tr} \, [ \, e^{\beta H } \,]$ . For solid, we assume simple ...
6
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1answer
167 views

Canonical ensemble: correlation function for quadratic potential energy

In this paper I can't understand the following A given system has the potential energy $ U(x_1,x_2,x_3)=k_1 x_1^2 + k_2 (x_2-x_1)^2 + k_3 x_3^2 $. Since the energy is quadratic, the correlation ...
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0answers
24 views

Defining Thermodynamic beta in unit of second

If I define Thermodynamic beta in unit of second. Does this mean that: Boltzmann constant $k$ is unit-less? $T$ is in units of frequency (Hz) or Kelvin $K$? In this case, is defining Thermodynamic ...
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0answers
12 views

ploting probability distribution of energy in Canonical ansambel [on hold]

To reproducing fig3.3 statistical mechanics pathria, probability density function of energy: $$p(E)\quad \alpha \quad e^{-\beta E} g(E) = e^{-\beta (U-TS)}~ exp{(-\frac{(E-U)^2}{2KT^2C_V})}$$ . I ...
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2answers
52 views

Canonical partition function and counting

That's a silly silly question, so my apologies, but in this moment I could not reach out! Let's have a system made of a particle reservoir $R$, and a subsystem $S$. The total particle number is $N$. ...
0
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1answer
38 views

If I prepare a state (density matrix) in Gibbs state, does it go to the lowest energy state at very low temperature?

Gibbs state is $$\rho_G=\frac{1}{Z} e^{-H/kT} = \sum_n \frac{1}{Z} e^{-E_n/kT}|E_n⟩⟨E_n| \, . $$ If $T$ goes to zero, does it mean the $\rho_G$ goes to the lowest energy state $|E_0⟩⟨E_0|$?
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1answer
27 views

How to prove that Gibbs state remains a gibbs state after evolution?

Gibbs state is $$ \rho_G=\frac 1Z e^{-H/kT}=\sum_n \frac 1Z e^{-E_n/kT}|E_n⟩⟨E_n|. $$. In wikipedia, it is said that a Gibbs state is an equilibrium probability distribution which remains invariant ...
2
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1answer
90 views

Two conflicting forms of equation of state of non-relativistic gas

I've run into two conflicting derivations of the equation of state of a non-relativistic gas. However, the derivations of the relativistic equation of state of both sources agree. I think maybe the ...
0
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1answer
78 views

Why Doesn't Einstein Get More Credit for Being the Father of Quantum Theory? [closed]

I'm not simply referring to the notion that Einstein treated the discrete emission and transference of energy (and matter) as "real" physical phenomena, but rather his major continuous role in the ...
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18 views

Moment direction and force [closed]

Replace the three forces acting on the plate by a wrench. Specify the magnitude of the force and couple moment for the wrench and the point P(x, y )where its line of action intersects the plate. FR=...
2
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1answer
53 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 ...
0
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1answer
45 views

Overcounting and what is indistinguishable about indistinguishable particles?

When getting the overcounting factor in statistical mechanics, how does one compute it? Let's say each property is unique in one aspect (a string with an unique address in pc memory for example). ...
5
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0answers
153 views

Thermodynamic equilibrium or thermal equilibrium and equipartition theorem

In all derivations of the equipartition theorem I can find a thermodynamic equilibrium distribution is used to show it's validity. But more vague sources (physics.stackexchange answer by Luboš Motl, ...
0
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1answer
243 views

Chemical Potential as a function of Temperature

I have considered an ideal fermi gas. Then, we can obtain an expression for chemical potential as a function of Temperature. I want to understand the physical significance to it or what it really ...
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44 views

Mixed Gas Absorbtion

Consider a gas misture that contains two type of atom, A and B. The gas is in equilibrium at temperature $T$. If on the surface of the gas container there are M sites that can absorb an atom gas, and ...
5
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2answers
185 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf j_{\...
0
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3answers
445 views

How to calculate critical temperature of the Ising model?

Can someone name a paper or book which calculates the critical temperature of the Ising model from scratch? It might be a book and should contain the necessary prerequisites. I have had a basic course ...
0
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1answer
17 views

Water evaporation rate: temperature vs humidity

I have a hot tub which I keep at 100 degrees F, and the water has "a lot" of dissolved salts in it. If I leave it open, will it evaporate faster when it is hot and humid outside, or when it is cold ...
5
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4answers
134 views

Could you filter coffee back to being pure water?

Okay, so coffee filters remove solid matter from the beverage, whilst leaving the remaining coffee intact for caffeiney goodness. But it's got me thinking. Is there a way we could filter the coffee ...
0
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2answers
37 views

Calculating the Total number of States for a microcanonical system

Please note before flagging, I do not need help solving as the math is simple algebra. Where I am lost is understanding what the math means and why/how it is applied. Problem 2.4 from Reif ...
1
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1answer
149 views

Periodic ground state 1-dim ising model

Good evening! I'm at the beginning of my study about the Ising model and it has been proposed to me this problem: Find all periodic ground-state configuration for the following one-dimensional Ising ...
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3answers
124 views

How Statistical Physics?

It's a common fact that in physics, we use statistics (or maybe probabilities ) to describe the behaviour of a system. It was from the statistical analysis of a system where quantum statistics arose ...
2
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2answers
102 views

Sufficient conditions for Equipartition Theorem to hold

I was wondering what are the sufficient conditions for the Equipartition Theorem. I know there is another question (For which systems is the equipartition theorem valid?) that somewhats answers this ...
2
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1answer
52 views

Generallized Canonical Ensemble - Isobaric Ensemble

I am trying to understand the way generalized canonical ensembles like the pressure ensemble are derived from the standard canonical ensemble. In the derivation for the standard form, one defines a ...
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0answers
39 views

Link Between the Density Operator and the Partition Function and Boltzmann Distribution in Quantum Statistical Mechanics

I have a very limited knowledge of statistical mechanics, but I seem to running into some related concepts for my background readings for the research project this summer. For example, see the ...
1
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0answers
55 views

Exact Solution of Ising Model in Open Boundary condition

What will be the exact expression of the partition function for 1d Ising model, if we consider open boundary case (This implies that the last spin in the sequence does not interact with the first spin)...
3
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4answers
294 views

Why would a Boltzmann brain be transient?

The Boltzmann brain idea as I understand it: suppose the universe has an infinite lifetime. Once heat death is achieved, there are no more large-scale structures to the universe -- everything is just ...
3
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2answers
42 views

Change of variables in canonical probability density

In K. Huang's book Statistical Mechanics, par. 7.2, the author writes the canonical partition function in a different way: $$Q = \frac{1}{N! h^{3N}} \int dp dq \ e^{-\beta H(p,q)} = \int_0^{\infty} ...
3
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55 views

Does a theory exist with a symmetry between a tachyonic and non-tachyonic mass points which preserves the normal laws of the mechanic?

Does a theory exist with a symmetry, which mirrors the tachyon mass points to non-tachyon mass points and vice versa? I think, it would be very beautiful, despite that there are strong theoretical ...
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49 views

Classical Grand canonical partition function derivation

Consider a classical grand canonical ensemble. Let $S_r$ be the reservoir entropy. Suppose it could be expanded at first order: $$S_r \approx S_r(E_t,N_t) + \frac{\mathrm dS_r}{\mathrm dE_i} \cdot ...