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

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What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
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1answer
155 views

Why is the $\langle v_{x}^{2} \rangle=\frac{1}{3} \langle v^2 \rangle$?

For a randomly moving particle. Or, I suppose that 1/3 could generalise to 1/n, where n is the non rotational degrees of freedom for that particle. Related reference Kinetic Theory of Gasses.
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3answers
971 views

Relation between statistical mechanics and quantum field theory

I was talking with a friend of mine, he is a student of theoretical particle physics, and he told me that lots of his topics have their foundations in statistical mechanics. However I thought that the ...
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1answer
71 views

Pressure change due to fan removing air from a non-airtight room

The following problem occurred to me today: Suppose a $100\mathrm{cfm}$ fan is pushing air out of a large room which is airtight except for a $10 \mathrm{cm}^2$ hole. The air pressure outside the ...
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0answers
110 views

What is meant by correlation propagation?

What is meant by correlation propagation in physics? I have an intuitive understanding but are there any introductory notes ( more mathematical oriented) and with some physical examples?
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2answers
289 views

Entropy: two explanations for the same quantity?

I studied thermodynamics and I saw the following definition for entropy: $$ \Delta S = \int_1^2 \frac{\text{d}Q}{T} $$ that we use to calculate $\Delta S$ for different types of transformations. In ...
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1answer
324 views

Entropy, flow of informations and fundamental theories

In the hierarchy of theories, first comes hamiltonian theory, from which one deduces kinetics theory, and at last thermodynamics and fluid theories. From a kinetics point of view, entropy and ...
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1answer
786 views

Why doesn't the percentage of oxygen in Earth's atmosphere diminish significantly with altitude?

According to numerous sources online, the percentage of oxygen is approximately the same at sea level and 10,000 meters. Since oxygen is heavier than nitrogen, shouldn't the percentage of oxygen ...
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1answer
213 views

What is theory of Free Energy Perturbation? How is it applicable to chemical science?

What is theory behind free energy perturbation? Is it way too difficult to understand? Can someone explain it in simple terms.
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3answers
610 views

number of microstates associated with two-level quantum systems

this is a very simple question, but apparently one that has no simple answer, at least from standard quantum mechanics theory I'm trying to figure the number of simple quantum states (microstates) of ...
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7answers
869 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 & ...
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0answers
94 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 ...
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3answers
1k 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 ...
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2answers
518 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 ...
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2answers
376 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 ...
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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 ...
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2answers
475 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?
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7answers
2k 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 ...
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0answers
109 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 ...
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1answer
54 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 ...
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3answers
335 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 ...
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2answers
1k 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 ...
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2answers
450 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 ...
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8answers
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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
141 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), ...
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2answers
284 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 ...
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4answers
302 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 ...
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1answer
650 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 ...
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1answer
508 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
129 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
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2answers
684 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?
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1answer
286 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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214 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, ...
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4answers
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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., ...
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2answers
284 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
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4answers
428 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 ...
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1answer
150 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 ...
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2answers
5k 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 ...
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2answers
460 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 ...
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2answers
157 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 ...
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3answers
239 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
8k 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 ...
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3answers
468 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 ...
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3answers
268 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, ...
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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 ...
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1answer
144 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 ...
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4answers
367 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
96 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?
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1answer
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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 ...
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3answers
288 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 ...