Questions tagged [statistical-mechanics]

The study of large, complicated systems employing statistics and probability theory to extract average properties and to provide a connection between mechanics and thermodynamics.

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Is information entropy the same as thermodynamic entropy?

Context In one of his most popular books Guards! Guards!, Terry Pratchett makes an entropy joke: Knowledge equals Power, which equals Energy, which equals Mass Pratchett is a fantasy comedian and ...
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Why are thermodynamic potentials minimised?

Why is it that, at equilibrium, certain potentials are minimised? That is, for a system at constant temperature and pressure, the Gibbs free energy is minimised, and for fixed volume and temperature, ...
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Prove that negative absolute temperatures are actually hotter than positive absolute temperatures

Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in ...
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16 votes
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How does radiation become black-body radiation?

Textbooks treat black body radiation as radiation in thermal equilibrium with its environment (more specifically - with a black body): Planck's formula is essentially derived from the partition ...
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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,...
75 votes
7 answers
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Is the Boltzmann constant really that important?

I read a book in which one chapter gave a speech about the fundamental constants of the Universe, and I remember it stated this: If the mass of an electron, the Planck constant, the speed of light, ...
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14 answers
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What is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
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32 votes
10 answers
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Can a single molecule have a temperature?

A show on the weather channel said that as a water molecule ascends in the atmosphere it cools. Does it make sense to talk about the temperature of a single molecule?
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11 votes
3 answers
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What is the correct relativistic distribution function?

General Statement and Questions I am trying to figure out the proper way to model a velocity/momentum distribution function that is correct in the relativistic limit. I would like to determine/know ...
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8 answers
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Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? I have never seen dissipation explained, although what I have seen a lot is descriptions of ...
propaganda's user avatar
9 votes
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Liouville's Theorem and Boltzmann equation for plasma

The Boltzmann equation for a plasma can be thought of as coming from a continuity equation in the 6 dimensional phase space of the plasma with coordinates $\left\{x,y,z,v_x,v_y,v_z \right\}$. So ...
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Could you please give an intuitive definition of chemical potential?

Could you please give an intuitive definition of chemical potential? It seems that it is an extremely important notion of physics but definitions are really vague.
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What's the most fundamental definition of temperature?

What's the most fundamental definition of temperature? Is it the definition concern about average energy, number of micro states, or what? By "fundamental", I mean "to be applied" in such general ...
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12 votes
2 answers
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Intuition behind Linked Cluster Theorem: connected vs. non-connected diagrams

Within statistical physics and quantum field theory, the linked cluster theorem is widely used to simplify things in the calculation of the partition function among other things. My question has the ...
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4 answers
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How to derive Shannon Entropy from Clausius Theorem?

I am studying Quantum Information now, and I need to understand the entropy of a quantum system. But before I go there, I need to understand Shannon Entropy which is defined as : $H(X) = -\sum_{i=1}^{...
Steve J.'s user avatar
67 votes
5 answers
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Is there a Lagrangian formulation of statistical mechanics?

In statistical mechanics, we usually think in terms of the Hamiltonian formalism. At a particular time $t$, the system is in a particular state, where "state" means the generalised coordinates and ...
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Why was the universe in an extraordinarily low-entropy state right after the big bang?

Let me start by saying that I have no scientific background whatsoever. I am very interested in science though and I'm currently enjoying Brian Greene's The Fabric of the Cosmos. I'm at chapter 7 and ...
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25 votes
7 answers
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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.
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3 votes
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Optimality of the Carnot cycle

It is well-known and is stated always and everywhere that the Carnot cycle is the most efficient thermodynamic cycle. Although stated as such it is rarely proven. One proof is in the article "...
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20 votes
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Could Navier-Stokes equation be derived directly from Boltzmann equation?

I know how to derive Navier-Stokes equations from Boltzmann equation in case where bulk and viscosity coefficients are set to zero. I need only multiply it on momentum and to integrate it over ...
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13 votes
11 answers
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Where does the irreversiblity came from if all the fundamental interaction are reversible?

There isn't too much to explain: We know that all fundamental forces are reversible then where does the irreversibility come from? Edit: The following is edit based on comments: Consider a block of ...
Young Kindaichi's user avatar
8 votes
5 answers
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Chance of objects going against greater entropy?

My book uses the argument that the multiplicities of a few macrostates in a macroscopic object take up an extraordinarily large share of all possible microstates, such that even over the entire ...
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56 votes
9 answers
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Is a spontaneous decrease in entropy *impossible* or just extremely unlikely?

I was reading this article from Ethan Siegel and I got some doubts about a sentence about entropy, specifically when Ethan explains the irreversibility of the conditions of the hot-and-cold room, as ...
Andy4983948's user avatar
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6 answers
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Is there a quasistatic process that is not reversible?

I have seen several questions and good answers on the link between reversible and quasistatic processes, such as here or here. However, these questions only adress one side of the problem : a ...
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Clear up confusion about the meaning of entropy

So I though, and was told, that entropy is the amount of disorder in a system. Specifically the example of heat flow and it flows to maximize entropy. To me this seemed odd. This seemed more ordered ...
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Absolute zero and Heisenberg uncertainty principle

I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position ...
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61 votes
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Why do we expect our theories to be independent of cutoffs?

Final edit: I think I pretty much understand now (touch wood)! But there's one thing I don't get. What's the physical reason for expecting the correlation functions to be independent of the cutoff? I....
Edward Hughes's user avatar
57 votes
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Is there any proof for the 2nd law of thermodynamics?

Are there any analytical proofs for the 2nd law of thermodynamics? Or is it based entirely on empirical evidence?
AIB's user avatar
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39 votes
8 answers
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How is Liouville's theorem compatible with the Second Law of Thermodynamics?

The second law says that entropy can only increase, and entropy is proportional to phase space volume. But Liouville's theorem says that phase space volume is constant. Taken naively, this seems to ...
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6 answers
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Is thermodynamics only applicable to systems in equilibrium?

So I was going through callen's thermodynamics book and their he says that thermodynamics is only applicable to systems which are in equilibrium and that naturally raised a few questions in my mind ...
Metric's user avatar
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19 votes
7 answers
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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 ...
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58 votes
2 answers
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Does entropy depend on the observer?

Entropy as it is explained on this site is a Lorentz invariant. But, we can define it as a measure of information hidden from an observer in a physical system. In that sense, is entropy a relative ...
veronika's user avatar
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Chemical potential

This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...
Student's user avatar
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12 votes
4 answers
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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 ...
orange_soda's user avatar
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6 votes
6 answers
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Is limited computational capacity a fundamental obstacle?

Statistical physics books often motivate the necessity of statistical/thermodynamic description by impossibility of calculating the trajectories of all the molecules (I speak of "trajectories&...
Roger V.'s user avatar
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63 votes
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How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
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27 votes
3 answers
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Is there some connection between the Virial theorem and a least action principle?

Both involve some 'averaging' over energies (kinetic and potential) and make some prediction about their mean values. As far as the least action principles, one could think of them as saying that the ...
esir's user avatar
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Why doesn't the entropy increase when two similar gases mix with each other?

Entropy increases when two substances mix with each other. For example, the entropy of mixing of two different gases are given by $$\Delta S= 2Nk\ln\frac{V_f}{V_i}\;.$$ But, the entropy doesn't ...
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27 votes
6 answers
8k views

Is gravity an entropic force after all?

Recently, there was a rapid communication published in Phys.Rev.D (PRD 83, 021502), titled "Gravity is not an entropic force", that claimed that an experiment performed in 2002 with ultra cold ...
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19 votes
2 answers
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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 ...
yrodro's user avatar
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17 votes
5 answers
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Understanding "natural variables" of the thermodynamic potentials using the example of the ideal gas

I'm struggling with the concept of "natural variables" in thermodynamics. Textbooks say that the internal energy is "naturally" expressed as $$ U = U(S,V,N)$$ For an ideal gas, I could take the ...
Marc's user avatar
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1 answer
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Are there necessary and sufficient conditions for ergodicity?

What are the necessary and sufficient conditions (if any) for ergodicity (or non-ergodicity)? I see for instance that some integrable systems are not ergodic. For instance a linear chain of harmonic ...
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9 votes
5 answers
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Please clarify how entropy increases when matter gravitationally coalesces

On John Baez's website, http://math.ucr.edu/home/baez/entropy.html, he discusses the problem of how entropy increases when a cloud of ideal gas collapses gravitationally (no black holes - keeping it ...
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59 votes
9 answers
8k views

How do different definitions of entropy connect with each other?

In many places over the Internet, I have tried to understand entropy. Many definitions are presented, among which I can formulate three (please correct me if any definition is wrong): Entropy = ...
Saeed Neamati's user avatar
45 votes
7 answers
8k 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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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 ...
Eka's user avatar
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13 votes
8 answers
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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 $0$ K, because that would imply that all molecules in the substance would stand perfectly still. He ...
Edward Stumperd's user avatar
12 votes
1 answer
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Phase space in quantum mechanics and Heisenberg uncertainty principle

In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state. In my book about statistical physics ...
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10 votes
4 answers
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Examples of density operators $\rho=\sum\limits_n p_n|\phi_n\rangle\langle\phi_n|$ in which the states $\{|\phi_n\rangle\}$ are not orthogonal

The set of quantum states $\{|\phi_n\rangle\}$ in the definition of the density operator $$\rho=\sum\limits_n p_n|\phi_n\rangle\langle\phi_n|$$ need not be orthonormal, and need not form a basis. But ...
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5 votes
3 answers
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Reference for statistical mechanics from information theoretic view

I am interested in knowing if some one here knows book/notes for statistical mechanics from the information theoretic viewpoint. Additional Request from user83014 "Jaynes wrote a paper called ...

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