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

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What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble?

In the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$: $$ \langle \hat n_r\rangle^{\pm} \ \propto \ ...
0
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0answers
75 views

What is known about the statistical mechanics of systems with normally distributed energies?

Consider a system taking on N states with energies $\epsilon \sim \mathcal{N}(\mu,\sigma^2)$. Are such systems well-studied in any context? I ask because I'd like to be able to take certain ...
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3answers
353 views

Is there really such a thing as an irreversible process?

If an isolated system goes from a state A to B, will it always eventually fluctuate back to state A? If not, give an simple example. Is it right to say that entropy only says that the probability ...
0
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1answer
222 views

How does physicists calculate the gravitational self collapsing force of a star?

The nuclear fusion taking place inside the stars opposes its gravitational self collapsing force. But, how does physicists calculate it? I just know the classical gravitational theory and not a bit of ...
1
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2answers
463 views

Why doesnt this violate 2nd law of thermodynamics?

Consider an ideal gas in a cylindrical container in a gravitational field, with a piston on top pushing down by gravity. The piston has some locking mechanism that locks it in place if it is displaced ...
3
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3answers
286 views

Configuration space of particles in the box

The notion of entropy says that we can count microstates that correspond to macrostate. But, I do not understand how this can be done. Does it imply that the state space is discrete (finite or ...
-1
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1answer
477 views

What is the difference between scale-free network and small-world network? [closed]

What is the difference between scale-free network and small-world network? I can't understand from the definitions around the web if they are both the same name for one thing. Do both follow a ...
4
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1answer
273 views

Percolation and number of phases in the 2D Ising model

Update. As my previous figure had conceptual mistakes I decided to change the picture to another, more instructive. After a long time I came back to try to understand an article on the Ising model. ...
6
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1answer
775 views

``What is life?'' by a physicist definition [closed]

The question is about defining ``What is life?'' in the field of Physics. Whether there is any (insightful) way of defining ``What is life?'' from physicists. There are pioneer works, including ...
2
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1answer
199 views

Meaning of Lagrange Multiplier in Ou-Yang and Helfrich's Shape equation for Membrane

Dear people in Physics Stackexchange, My question is mostly related to the following papers: U. Seifert, Z. Phys. B 97, 299 (1995). "The concept of effective tension for fluctuating vesicles". U. ...
15
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5answers
2k views

Why isn't absolute $0 K$ temperature possible?

So $T$ is defined as $$T = \left(\frac{\partial E}{\partial S}\right)$$ and $S$ is defined as $$S = k_B \ln \Omega$$ where $\Omega$ is the number of accessible states of the system for a given ...
15
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7answers
2k views

How do you prove the second law of thermodynamics from statistical mechanics?

How do you prove the second law of thermodynamics from statistical mechanics? To prove entropy will only increase with time? How to prove? Please guide.
2
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0answers
109 views

How to formally write down the Boltzmann equation?

Can someone write down the Boltzmann equation, not neglecting any of the variables of the involved functions and integrals? Specifically, how to concisely capture the "primed" variables in a sensible ...
7
votes
1answer
592 views

The virial theorem and a delta function potential

So the virial theorem tells us that: $2\langle T\rangle = \langle \textbf{r}\cdot\nabla V\rangle$. Now I was wondering what would happen if V has te form: $V(\textbf{r}-\textbf{r}') = ...
3
votes
1answer
2k views

Equation of state of a rubber band

I have the following question that I attached in png format. I have done part (a), but I am having difficulties in part (b) when I proceed according to the book. I have non zero tension at ...
6
votes
1answer
270 views

Is it always possible to express an operator in terms of creation/annihilation operators?

I'm referring to "Path integral approach to birth-death processes on a lattice", L. Peliti, J. Physique 46, 1469-1483 (1985), available at: http://people.na.infn.it/~peliti/path.pdf The article is ...
7
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3answers
4k views

What are the six degrees of freedom of the atoms in a solid?

A monoatomic ideal gas has heat capacity $C_v=1.5$ which comes from the three translational degrees of freedom. For solids at high temperature, $C_v=3$, implying six degrees of freedom. What are ...
14
votes
1answer
465 views

Does this type of phase transition exist?

The short version of this question is: Is there, or could there be, a system with a phase transition where adding a small amount of heat causes a discontinuous jump in its temperature? Below are ...
1
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2answers
507 views

naive question on Boltzmann equation and conservation laws

The Boltzmann equation in absence of external force reads: $\frac{\partial f}{\partial t} + \vec{v} \cdot \frac{\partial f}{\partial \vec{r}} = \left( \frac{\partial f}{\partial t}\right)_{coll}$ ...
1
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2answers
215 views

Entropy Maximization using undetermined multipliers

This is from Problems in Thermodynamics and Statistical Physics by P.T. Landsberg A system can be in any one of N states. Using the method of undetermined multipliers to show for the maximum ...
0
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0answers
76 views

Is it possible to derive fermi-dirac or bose-einstein statistics using quantum operator formulations?

I've been looking through theory on identical particles to get a better grasp of the uncertainty principle but it would be very interesting if these results could be extracted from the formalism as ...
0
votes
1answer
208 views

Justifications for different Monte Carlo trial moves

Why do we perform different trial moves in Monte Carlo simulations in Statistical Mechanics? For example, in NVT ensemble simulations, Why only atom displacement moves? In NPT ensemble, why do we need ...
28
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3answers
25k views

First and second order phase transitions

Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article (at the time of writing) starts by explaining that Ehrenfest's original definition ...
1
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1answer
564 views

Why do pressure and chemical potential depend on temperature, instead of having symmetric definitions?

I'm following an introduction to statistical mechanics and have seen the following definitions for fundamental temperature, pressure and chemical potential respectively: $$\frac{1}{\tau} := \left( ...
2
votes
1answer
1k views

Practical difference between canonical and grand canonical ensembles

I'm currently doing some calculations which require evaluating various standard thermal expectation values in the canonical ensemble (both bosons and fermions). Now, in order to make my theoretical ...
0
votes
2answers
149 views

Grand canonical ensemble with interaction, simulation doubts

First of all, this is a follow-up of my first question. The idea is the same, every state would consist of some particles in a line (with an energy associated) and the particles can not be nearer than ...
10
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1answer
957 views

Definition of phase transitions in statistical mechanics

Phase transitions in statistical mechanics are usually taught by working through a bunch of examples. I decided to try and think about them from a more "fundamental" point of view - but I've run into ...
3
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1answer
2k views

What is off-diagonal long range order in superfluid?

From Wikipedia: [...]Off-diagonal long-range order (ODLRO) [...] exists whenever there is a macroscopically large factored component (eigenvalue) in a reduced density matrix of any order. How to ...
1
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1answer
780 views

Rate of effusion in kinetic molecular theory?

According to the kinetic molecular theory obeying Maxwell-Boltzmann distribution of speeds, the rate of effusion through a pinhole of area $A$ is $$R=\frac{PA}{\sqrt{2\pi M R T}}$$ where $M$ is the ...
1
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1answer
467 views

detailed balance in the context of the ising model

I am having a very basic problem understanding the idea of detailed balance, particularly in the context of the Ising model. Most references I have found contain the following phrase: "In ...
4
votes
0answers
90 views

Can the correlation for the Potts model be bounded?

I am studying a $d$-state Potts model. A configuration $\sigma$, which assigns for each $x\in \mathbb{Z}^2$ a value $\sigma(x)\in [1,2,\ldots,d]$, with the probability on a finite lattice defined as ...
8
votes
1answer
312 views

Any open areas to work in non equilibrium thermodynamics for a Phd student? [closed]

I see that many papers written on fundamentals of thermodynamics(theory) nowadays are by some old professors somewhere(there may be exceptions). Most active young faculty don't seem to be seriously ...
6
votes
1answer
243 views

Is “detailed balance” equivalent with a continuity equation in state space?

I have a talk tomorrow in which detailed balance is needed and I don't want to bore my audience with elaborate explanations for it so I'm looking for simpler explanations. As far as I understood it ...
2
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1answer
200 views

Research on ground state configuration of Ising model

I want to do mathematical research (algorithm construction and mathematical analysis) on Ising model ground state configuration. From what I know, the state of art research is using graph theory ...
6
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4answers
949 views

Entropy as an arrow of time

From what I understand, entropy is a concept defined by the experimentalist due to his ignorance of the exact microstate of a system. To say the number of accessible microstates $W$ of the universe is ...
10
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2answers
523 views

Casimir effect as an entropic force

When I first learned about the depletion interaction, my initial reaction was that it looks very similar to the Casimir effect. On making this remark to the professor, he replied somewhat mystically: ...
0
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1answer
1k views

Calculating the ideal mixing entropy using Gibbs' entropy formula

Two distinguishable gases are in separate volumes $xV$ and $(1-x)V$ $(x\in [0,1])$ respectively, and the number of particles on each side is $xN$ and $(1-x)N$ respectively. The volumes are separated ...
3
votes
1answer
184 views

Boltzmann distribution with interaction between particles?

First of all, I would like to apologize in advance if I make stupid mistakes. I am a mathematician and I am trying to apply the Boltzmann distribution to places where I am not sure if it is applicable ...
6
votes
1answer
403 views

A thermodynamic transformation that can be represented by a continuous quasistatic path in its state space may still be irreversible. Why?

A thermodynamic transformation that has a path (in its state space) that lies on the surface of its equation of state (e.g., $PV=NkT$) is always reversible (right?). However, if the path is a ...
3
votes
1answer
1k views

Should entropy have units and temperature in terms of energy? [duplicate]

I've been thinking about entropy for a while and why it is a confusing concept and many references are filled with varying descriptions of something that is a statistical probability (arrows of time, ...
1
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2answers
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 ...
1
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3answers
685 views

What is the energy of a standing EM wave? Is it probabilistic?

In a cavity, the standing wave will constructively interfere with itself, so its energy gets higher while the oscillator is still vibrating. Since the vibration time is not a constant value, and ...
0
votes
1answer
76 views

Can a distribution with sharper energy maximum than the exp-function give an equivalent theory?

Because for many particles the distribution $\varrho\sim\mathrm e^{-\beta\ H}$ has an extremely sharp maximum, the expectation values of the canonical ensemble agrees with that of the microcanonical ...
1
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0answers
44 views

Ergodicity Breaking in Supercooled Liquids

What is a ergodic system? What is Onset temperature of ergodicity breaking in super cooled liquids when we go towards lower temperature?
2
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1answer
418 views

How to derive the two-term approximation for the Boltzmann equation?

Starting with the Boltzmann equation in terms of $f(t,\vec v,\vec x)$ or $f(t,\vec v)$ http://en.wikipedia.org/wiki/Boltzmann_equation $$\left(\frac{\partial}{\partial t} + \vec{v} \, ...
0
votes
1answer
292 views

Entropy of a particle with two energy states [closed]

A particle has two energy states having energies $E_0$ and $E_1$ with degeneracies $g_0$ and $g_1$. The respective probabilities are $p_1$ and $p_2$. What is the entropy in terms of $p_1$, ...
1
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2answers
331 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 ...
7
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2answers
849 views

The statistical nature of the 2nd Law of Thermodynamics

Ok, so entropy increases... This is supposed to be an absolute statement about entropy. But then someone imagines a box with a 10 particle gas, and finds that every now and then all particles are in ...
0
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0answers
47 views

What is Verlinde's statistical description of gravity as an entropic force? [duplicate]

What is Verlinde's statistical description of gravity as an entropic force leads to the correct inverse square distance law of attraction between classical bodies?
2
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0answers
84 views

Can classical orders coexist with quantum orders?

For example, the ground state of the antiferromagnetic(AFM) Heisenberg model $H=J\sum_{<ij>}\mathbf{S}_i \cdot \mathbf{S}_j(J>0)$ on a 2D square lattice is a Neel state, which is a classical ...