Questions tagged [statistical-mechanics]

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

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What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?

This question was listed as one of the questions in the proposal (see here), and I didn't know the answer. I don't know the ethics on blatantly stealing such a question, so if it should be deleted or ...
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If we had a "perfectly efficient" computer and all the energy in the Milky-way available, what number could it count to?

The idea for this question comes from an example in cryptography, where supposedly 256-bit symmetric keys will be enough for all time to come (brute-forcing a 256-bit key is sort-of equivalent to ...
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First and second order phase transitions

Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article starts by explaining that Ehrenfest's original definition was that a first-order ...
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Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms try to ...
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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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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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If liquid and gas are both chaotic states of matter, what's the difference between them on the molecular level?

I'm a laywoman in physics and recently found myself pondering about the matter reflected in the title of this post. To make my question more precise from the mathematical standpoint, let's suppose ...
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Systematic approach to deriving equations of collective field theory to any order

The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
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I have problem understanding entropy because of some contrary examples

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 = ...
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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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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 ...
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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....
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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?
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Can Lee-Yang zeros theorem account for triple point phase transition?

Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost become a standard ingredient of any comprehensive statistical mechanics textbook. If the volume tends to infinity, ...
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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 ...
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What's the rigorous definition of phase and phase transition?

I always feel unsure about the definitions of phase and phase transition. First, let's discuss in Laudau's paradigm. For example, some people say that phase is classified by symmetry. Some people say ...
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What are some critiques of Jaynes' approach to statistical mechanics?

Suggested here: What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis? I was wondering about good critiques of Jaynes' approach to statistical ...
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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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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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Why is the partition function called ''partition function''?

The partition function plays a central role in statistical mechanics. But why is it called ''partition function''?
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Why isn't the entropy of gas infinite if there are infinite microstates available?

How could it be that the entropy of gas is not infinite? If we use the formula $S=k\ln(\Omega)$ we get infinity because there are an infinite number of possible situations (because there are infinite ...
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Homemade salad dressing separates into layers after it sits for a while. Why doesn't this violate the 2nd law of thermodynamics?

The oil, vinegar and other liquids in homemade salad dressing separate into layers after sitting for a while, making the mixture become more organized as time evolves. Why doesn't this violate the ...
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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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Is there a thermodynamic limit on how efficiently you can solve a Rubik's cube?

Suppose I build a machine which will be given Rubik's cubes that have been scrambled to one of the $\sim 2^{65}$ possible positions of the cube, chosen uniformly at random. Is it possible for the ...
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The unreasonable effectiveness of the partition function

In a first course on statistical mechanics the partition function is normally introduced as the normalisation for the probability of a particle being in a particular energy level. $$p_j=\frac{1}{Z}\...
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$(\mu,P,T)$ pseudo-ensemble: why is it not a proper thermodynamic ensemble?

While teaching statistical mechanics, and describing the common thermodynamic ensembles (microcanonical, canonical, grand canonical), I usually give a line on why there can be no $(\mu, P, T)$ ...
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When I put my hand on a hot solid why don't the particles transfering heat to my hand exert a force on it?

When I put my hand on a hot metal (say) solid, I can feel my hand heating up. I suspect this is caused mostly by particles (electrons, atoms, ...?) from the solid colliding with the particles that ...
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Examples of important known universality classes besides Ising

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical ...
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If temperature is amount of kinetic energy of particles, then how can there be a cold breeze? [duplicate]

When we put hands on A/C it gives cold winds. These winds have high kinetic energy but low temperature. How ? *don't confuse with A/C being heat pump , just an example, take antarctic blizzards. I can'...
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Can a broken egg spontaneously reassemble itself (as in the video)?

According to the fluctuation theorem, the second law of thermodynamics is a statistical law. Violations at the micro scale, therefore, certainly have a non-zero probability. However, the application ...
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Why can't many models be solved exactly?

I have been told that few models in statistical mechanics can be solved exactly. In general, is this because the solutions are too difficult to obtain, or is our mathematics not sufficiently advanced ...
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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 ...
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Intuition for when the replica trick should work and why it works

I am a graduate student in mathematics working in probability (without a very good background in physics honestly) and I've started to see arguments based on computations derived from the replica ...
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Motivation for the use of Tsallis entropy

Every now and again I hear something about Tsallis entropy, $$ S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1} $$ and I decided to finally get around to investigating it. I haven't ...
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Why don't things get destroyed by gas molecules flying around?

Gas molecules go at an insane velocity, and though they are miniscule, yet there is a LOT of them. Of course, because of all these molecules hurtling around, there is air pressure; yet if you envision ...
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Why does a critical point exist? [duplicate]

I still cannot fully comprehend the essence of a critical point on phase diagrams. It is usually said in textbooks that the difference between liquid and gaseous state of a substance is quantitative ...
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What is the difference between thermodynamics and statistical mechanics?

What is the difference between thermodynamics and statistical mechanics?
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How is temperature defined, and measured?

In questions like this one, temperatures of millions of degrees (Celsius, Kelvin, it doesn't really matter at that point) are mentioned. But, what does it mean exactly? What is measured, and how? As I ...
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How can fast moving particles gain energy from slow moving ones?

Imagine a large diameter piston filled with water connected to a small funnel. When you press on the piston slowly but with considerable force the water will move very quickly from the funnel in form ...
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How is Liouville's theorem compatible with the Second Law?

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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What is the definition of temperature, once and for all? [duplicate]

Can someone please explain to me what the formal definition of temperature is? Neither my textbook, nor my professor, nor any of the online sources I've checked are able to give me a proper ...
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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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What is the difference between scale invariance and self-similarity?

I always thought that these two terms are some kind of synonyms, meaning that if you have a self-similar or scale invariant system, you can zoom in or out as you like and you will always see the same ...
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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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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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Why is the fundamental postulate of statistical mechanics true?

As I'm sure folks here know, the principle of equal a priori probabilities, sometimes called the fundamental postulate of statistical mechanics, states the following: For an isolated system with an ...
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Does it make sense to ask how many of the molecules you are inhaling Caesar exhaled in his last breath?

There is a nice example of a Fermi estimation question where you ask: How many of the molecules which Julius Caesar (or Jesus, Muhammad, etc. - anyone who died a long time ago) exhaled in their dying ...
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How do you prove $S=-\sum p\ln p$?

How does one prove the formula for entropy $S=-\sum p\ln p$? Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law ...
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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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Are there any modern textbooks on statistical mechanics which don't ignore Gibbs' analysis of the microcanonical ensemble?

I have lately been reading Gibbs' book Elementary Principles in Statistical Mechanics, and I'm surprised how much in that book seems to have been ignored by later textbook writers. In particular, ...

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