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

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2answers
410 views

Maxwell-Boltzmann distribution and total energy per unit volume

We know that $$n(E) ~=~ \frac {2 \pi (N/V)}{(\pi k_B T)^{3/2}} E^{1/2} e^{-E/(k_B T)} dE,$$ where $V$ is total volume. If then, how do we derive total energy per unit volume from this equation?
21
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7answers
986 views

How is $\frac{dQ}{T}$ measure of randomness of system?

I am studying entropy and its hard for me to catch up what exactly is entropy. Many articles and books write that entropy is the measure of randomness or disorder of the system. They say when a gas ...
2
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0answers
96 views

Randomly sampling a “well-mixed” solution of Brownian particles

I place $N$ Brownian particles in $V$ liters of solution, shake until I assume that the particles are "well-mixed", and sample and randomly sample an $S$ liter volume. What is the probability ...
1
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1answer
51 views

In which way is decoherence not symmetric between the two considered systems?

If a quantum system interacts with a "big" quantum system, you have dephasing. The models of decoherence all have this atog aproach to them, about what is to understood of the interaction of the ...
7
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3answers
300 views

Is particle number a problem for formulating statistical physics in a mathematically rigorous manner?

Quantities like the chemical potential can be expressed as something like $$\mu=-T\left(\tfrac{\partial S}{\partial N}\right)_{E,V}.$$ Now the entropy is the log some volume, which depends on the ...
3
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2answers
886 views

Latent heat vs temperature of phase transitions?

Is the latent heat associated with phase transitions correlated with the temperature at which they occur? The latent heat is related to the difference in energy between the two phases, and the ...
11
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2answers
420 views

Can $10^{23}$ stars be treated with methods of statistical mechanics?

Statistical mechanics is used to describe systems with large number of particles ~$10^{23}$. The observable universe contains between $10^{22}$ to $10^{24}$ stars. Can we treat those many stars as a ...
5
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7answers
2k views

Is it theoretically possible to reach 0 kelvin?

I'm having a discussion with someone. I said that it is -even theoretically- impossible to reach 0K, because that would imply that all molecules in the substance would stand perfectly still. He said ...
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1answer
130 views

Where is the critical moment where the microcanonical ensemble enters the justification for the equilibium state?

As explained in many books, for the microscopic justification of the second law of thermodynamics (lets formulate it as the total entropy takes maximum among all possible exchanges of two systems), ...
2
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2answers
253 views

Average Neighbouring Impurity Separation in a Random 1D chain [closed]

I have a finite and discrete 1D chain (edit: linear chain, i.e. a straight line) of atoms, with unit separation, with a set number of impurities randomly distributed in the place of these atoms in ...
7
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4answers
254 views

Is energy extensivity necessary in thermodynamics?

Given a partition of a system into two smaller systems, the energy $U$ is devided into $U_1$ and $U_2$, with $$U=\mathcal{P}(U_1,U_2):=U_1+U_2,$$ so that $U_2$ is given by $U-U_1$. Here the ...
6
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1answer
487 views

Mean-field theory in 1D Ising model

A mean-field theory approach to the Ising-model gives a critical temperature $k_B T_C = q J$, where $q$ is the number of nearest neighbours and $J$ is the interaction in the Ising Hamiltonian. Setting ...
4
votes
1answer
390 views

Integration of partition-function over many momentum variables

My integral looks like $$Z(\beta) = \frac{1}{h^3}\int d^3p\ \exp{\left(-\frac{\beta}{2m}\sum^{3N}_{i=1}p_i^2\right)}.$$ I'm confused about how to integrate over seemingly 3N variables in only a ...
5
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0answers
111 views

What is the proper time used in relativistic non equilibrium statistical physics?

In the literature one often finds covariant relativistic generalizations of classical non equilibrium statistical equations (Boltzmann, Vlasov, Landau, fokker-planck, etc...) but I wonder what is the ...
3
votes
2answers
544 views

Where do the terms microcanonical, canonical and grand canonical (ensemble) come from?

Where do the terms microcanonical, canonical and grand canonical (ensemble) come from? When were they coined and by whom? Is there any reason for the names or are they historical accidents?
2
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1answer
243 views

Partition function of an interacting gas

By reading an article, I found a partition function that, according to the author, describes an interacting with random variables as coupling constant. $$Z =\int \mathrm{d} \lambda_i ...
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2answers
177 views

What is the origin of nonconservative force?

My understanding about conservative force is a force that its work is independent of path such that we can construct another form of the work called potential to make our life easier. For friction, ...
6
votes
4answers
3k views

Why is the canonical ($NVT$) ensemble often used for (classical) molecular dynamics (MD) simulations?

Molecular dynamics (MD) simulation is a common approach to the (classical) many-body problem. It relies on integration of Newton's equations of motion to simulate the trajectories of many (e.g., ...
7
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2answers
232 views

Effect of boundary conditions on partition functions

While computing partition functions in statistical mechanics models (say) on a 2d lattice one usually makes use of "circular boundary conditions" which thus gives the lattice topology of a torus. It ...
4
votes
4answers
337 views

Friction at zero temperature?

By the fluctuation-dissipation theorem (detailed-balance for Langevin equation), $$\sigma^2 = 2 \gamma k_B T$$ where $\sigma$ is the variance of noise, $\gamma$ is a friction coefficient, $k_B$ is ...
8
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1answer
118 views

Deviation from power law distribution of earthquakes

One of the most accepted frameworks for the relationship between the magnitude and frequency of an earthquake is that of the critical phenomena. In this framework, the magnitude of events must be ...
6
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2answers
3k views

What is the relationship between Energy, Entropy, and Information?

What is the relationship between Energy, Entropy, and Information? I read this - What Is Energy? Where did it come from? - and the top answer says that 'energy' is an abstract number that is a ...
4
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2answers
359 views

How and why can random matrices answer physical problems?

Random matrix theory pops up regularly in the context of dynamical systems. I was, however, so far not able to grasp the basic idea of this formalism. Could someone please provide an instructive ...
2
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2answers
145 views

May molecules of ideal gases have an inner structure?

The following question is probably very elementary: whether molecules of ideal gases may have optic properties? As far as I understand, when one discusses optic properties, one assumes that molecules ...
2
votes
3answers
214 views

Misconception about the expectation of a quantum system

For a two-level quantum system with energy eigenstates $|\phi_1\rangle$ and $|\phi_2\rangle$ at finite temperature, we can write a general state as ...
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5answers
4k views

Recommendations for Statistical Mechanics book

I saw Book recommendations No reference to Statistical Mechanics there. I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly ...
6
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3answers
406 views

Non equilibrium statistical mechanics

A question kept bothering me about the Non-Equilibrium Statistical mechanics, can somebody give a simple description of how one approaches this subject. Is there a exact formalism, as we have for ...
3
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3answers
238 views

What are some creative illustrations of the nature of dissipative forces?

I'm teaching a conceptual introduction to physics for American 13-15 year old students this summer. One of the main ideas I want to hit on is the relationship between energy conservation, ...
0
votes
1answer
972 views

Ideal gas with two kinds of particles, Grand canonical partition function

Consider an ideal gas contained in a volume V at temperature T. If all particles are identical the Grand canonical partition function can be calculated using $$Z_g(V,T,z) := \sum_{N=0}^\infty z^N ...
1
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1answer
141 views

Lacking of scale and distribution moments

Given a physical random variable x, $E(x)$ and $E((x-<x>)^2)$ defines mean and variance. From a statistical point of view variance represents the statistic error (isn't it?). If variance is not ...
1
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4answers
290 views

Deriving Statistical Mechanics laws from Quantum Mechanics?

Since the law of individual molecule is governed by Quantum Mechanics, and the interaction of large number of molecule is governed by Statistical Mechanics, can we derive Statistical Mechanics from ...
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1answer
91 views

Rainfalls and critical phenomena

By definition, rainfalls are transitions from vapor state to liquid state of water. I can say that "by definition" rainfalls must viewed as critical phenomenon?
6
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1answer
972 views

Are there good resources explaining mean field approximation?

I am a computer science master student. In a statistical learning theory course I am taking, mean field approximation was introduced to approximately solve non-factorizable Gibbs distributions that ...
2
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3answers
238 views

Slow thermal equilibrium

I have a question which is inspired by considering the light field coming off an incandescent lightbulb. As a blackbody radiation field, the light is in thermal equilibrium at temperature $T$, which ...
0
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1answer
233 views

How “to take” this integral?

When I learned anharmonic model of crystal, I read that considering anharmonic oscillations and Boltzmann distribution for the "atoms" of crystal we can get the dependence of distance between the ...
5
votes
1answer
1k views

Hit a bottle of beer on the top with another causes the first to spit all the gas, why?

So, on the other day me and my colleges were discussing the following phenomena: Pick two open bottles of beer. With the bottom of the first, hit the second on the bottleneck, in the following way: ...
3
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0answers
108 views

Qualitative argument to determine energy of defects

In a book of "LES HOUCHES - Critical Phenomena, Random systems, Gauge theories" the author Frolich says that: 2D In two dimensions, the mean energy of an isolated point defect in a square area of ...
1
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1answer
177 views

What kind of phases nanoparticles have (gas-solid-liquid)?

If a phase transition requires a number of particles that is in the TD-limit, can nanoparticles (~10 atoms) have phase transitions? What kind of phases and transitions nanoparticles have?
4
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3answers
352 views

How many particles is needed to observe a phase transition?

This is a question that was rised when we were discussing "what is melting actually". How many particles you need to form a liquid or solid. I have some remarks to point out what I want to know. Q: ...
3
votes
1answer
169 views

How is the dynamic equilibrium nature of fermi-dirac distribution of particles facilitated?

I read this in Kittel: Introduction to Solid State Physics about deriving that product of electron and hole concentration as independent at a given temperature by the law of mass action. For this ...
3
votes
2answers
303 views

What fraction of electrons is captured in semiconductor defects?

I'm having trouble with the following exercise: Some point defects (impurities, holes, etc.) in semiconductors can trap an electron in a localized state with energy $E_{1}$ and spin $-1/2$. A second ...
0
votes
3answers
1k views

The meaning of scale invariance in power law distribution

A function $f(ax)$ that satisfies $$ f(ax)=a^\Delta f(x)\,\,\, (\Delta \in R) $$ is said to be scale invariant. The most general function $f(x)$ that satisfies the previous condition is of the form ...
14
votes
1answer
332 views

How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...
0
votes
2answers
217 views

How was transformed an integral below?

I know how transform an integral below, $$ \iint f(\mathbf v_{1})f(\mathbf v_{2})d^3\mathbf v_{1}d^3\mathbf v_{2}, $$ using relative speed coordinates: we just use $$ m_{1} \mathbf v_{1} + ...
4
votes
1answer
187 views

Scale invariance in sandpile model and forest fire model

I asked a similar question but the wrong way here. Because my intention was to ask about non thermodynamic system, i will be more specific: What is the relation between critical behaviour and the ...
2
votes
1answer
242 views

Scale invariance and self organized criticality

On wikipedia i have found this statement: In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems which have a critical point as an attractor. Their ...
5
votes
1answer
441 views

Percolation in a 2D Ising model

For a 2D Ising model with zero applied field, it seems logical to me that the phases above and below T_c will have different percolation behaviour. I would expect that percolation occurs (and hence ...
2
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2answers
590 views

Ideal gas in a vessel: kinetic energy of particles hitting the vessel's wall

Reading Landau's Statistical Physics Part (3rd Edition), I am trying to calculate the answer to Chapter 39, Problem 3. You are supposed to calculate the total kinetic energy of the particles in an ...
2
votes
1answer
140 views

renormalization group in d=3

Do we really understand why the renormalization group in $d=2+\varepsilon$ and $d=4-\varepsilon$ taking $\varepsilon=1$ gives "good" values for critical exponents in $d=3$? Are they exceptions? Is it ...
4
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1answer
419 views

upper critical dimension in field theory

Is there field theory which describe a second order phase transition without upper critical dimension ? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.