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

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7
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726 views

Is it wrong to talk about wave functions of macroscopic bodies?

Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not? For example in the "Statistical Physics, Part I" by Landau & ...
1
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0answers
93 views

usage of partition function in some number of particles in one-dimensional axis

I just learned some introductory quantum meachnics, but not statistical mechanics, so I am curious how partition functions would be used in the following case: Suppose there are three particles in ...
5
votes
3answers
875 views

Is temperature an extensive property, like density?

I was thinking about it some time ago, and now that I've discovered this site I would like to ask it here because I couldn't work it out then. I know that the higher temperature the air in my room ...
3
votes
2answers
411 views

Time to establish saturated vapour pressure above liquid

Thought experiment - a liquid is in a closed container in equilibrium with its vapour, and then suddenly all the vapour is pumped away. Switch off the pump so that instantaneosuly there is no vapour ...
2
votes
2answers
326 views

Convergance of a system to Boltzmann distribution

Consider a system with finite-dimension state X and energy E(X), with dynamics which follow the Langevin equation $\frac{dX}{dt}=-\nabla_X{E(X)}+\eta(t)$ where $\eta$ is white noise ...
5
votes
1answer
1k views

What does the concept of phase space mean in particle physics?

I came across the concept of phase space in statistical mechanics. How does this concept come about in particle physics? Why was it introduced and how is it used? What does it mean when ...
1
vote
2answers
424 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
votes
7answers
1k 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
votes
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
vote
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
votes
3answers
302 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
votes
2answers
935 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
votes
2answers
421 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
votes
7answers
3k 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 ...
1
vote
1answer
131 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
votes
2answers
256 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
votes
4answers
261 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
votes
1answer
503 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
413 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
votes
0answers
112 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 ...
4
votes
2answers
567 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
votes
1answer
246 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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vote
2answers
178 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
votes
2answers
239 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
358 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
votes
1answer
124 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
votes
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
votes
2answers
374 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
votes
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
217 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 ...
7
votes
5answers
4k 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 ...
6
votes
3answers
412 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
votes
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
1k 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
vote
1answer
142 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
vote
4answers
295 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 ...
1
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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
votes
1answer
1k 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
votes
3answers
242 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
votes
1answer
234 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
2answers
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
votes
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
vote
1answer
179 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
votes
3answers
355 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
171 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
311 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
340 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
220 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} + ...