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

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Minimum connectivity required for mean field to be a good approximation?

In spin models, it is known that mean field becomes a better approximation as the connectivity increases. My question is: Is there an estimate for the threshold connectivity (as a function of the ...
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2answers
257 views

Classical and Semi-classical treatments of the ideal gas

In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the ...
6
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1answer
353 views

few fermions in a harmonic trap — position density matrix from diagrammatics

I'm trying to calculate the momentum distribution of a 1D system of non-interacting identical fermions in a harmonic trap. Given Feynman's answer (from his Statistical Mechanics book) for the ...
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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 ...
6
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1answer
224 views

Nonextensive statistical mechanics

I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times ...
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139 views

Is the stability matrix of a linearised RG flow always diagonalisable?

This is a follow up on "Why are the eigenvalues of a linearized RG transformation real?". My question is simple: Is there some physical (or mathematical) reason for the stability matrix of ...
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218 views

How does statistical mechanics predict that hot air rises?

Does hot air rise -- from a statistical-mechanical viewpoint Question #6329 asks whether and why hot air rises. The consensus answer is straightforward: - hot air is less dense than cold air - ...
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203 views

2d Ising model in CFT and statistical mechanics

When I recently started to read about conformal field theory, one of the basic examples there is the so called Ising model. It is characterized by certain specific collection of fields on the plane ...
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566 views

Is Feynman talking about the Zeroth Law of Thermodynamics?

In Volume 1 Chapter 39 of the Feynman Lectures on Physics, Feynman derives the ideal gas law from Newton's laws of motion. But then on page 41-1, he puts a caveat to the derivation he has just ...
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94 views

Does the Standard Model plasma develop a spontaneous magnetisation at finite temperature?

Reference: arXiv:1204.3604v1 [hep-ph] Long-range magnetic fields in the ground state of the Standard Model plasma. Alexey Boyarsky, Oleg Ruchayskiy, Mikhail Shaposhnikov. The authors of this paper ...
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225 views

Drawing the RG flow diagram

In real-space renormalization group how does one find the complete RG flow exactly, (not schematically)? I understand it needs to be done on a computer. For example, I have the ising model on a ...
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210 views

Are there known turbulent nonlinear equations where the cascade is a thermal gradient?

In a recent answer (here: The equipartition theorem in momentum space ), I suggested that if you have an appropriate first order equation (in the answer I used a second order equation, but it is more ...
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282 views

Tsallis entropy and other generalizations

If I am given a system, which I might have to describe using a generalized entropy, like the "q-deformed" Tsallis entropy, do I have to fit q from experiment or might I know it beforehand? How do I ...
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3k views

Is temperature in vacuum zero?

From Wikipedia entry on Kinetic Theory The temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms. Now if I remove all the particles from the box shown ...
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5answers
2k views

Second law of Thermodynamics: Why is it only “almost” always true that entropy is non-decreasing? [duplicate]

Wikipedia - Second law of thermodynamics: ...the entropy of any closed system not in thermal equilibrium almost always increases. I understand that the second law of thermodynamics is based on ...
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3answers
861 views

Why is Avogadro's hypothesis true?

Why is the number of molecules in a standard volume of gas at a standard temperature and pressure a constant, regardless of the molecule's composition or weight? Let's say I have a closed box full of ...
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2answers
375 views

Why energy at room temperature $= kT$ and not $(3/2)kT$ [duplicate]

I always see that a room temperature of $T=300\,\text{K}$ corresponds to an energy of $k_BT \approx \frac{1}{40}\,\text{eV}$. But shouldn't it be $\frac{3}{2}k_BT$ since the molecules in the air have ...
5
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291 views

Strange definition of microcanonical partition function

I always thought that the microcanonical partition function would measure the number of states that correspond to some fixed energy. Despite, I found in this paper (equation 3.4) that we integrate ...
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414 views

Axioms behind entropy!

The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of ...
5
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153 views

Bose-Einstein condensate for general interacting systems

There is Bose-Einstein condensate (BEC) for non-interacting boson systems. Can we prove the existence of BEC for interacting systems?
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795 views

Are negative temperatures typically associated with negative absolute pressures?

Negative temperatures and negative absolute pressures are both possible in physical systems. Negative temperatures arise in (for example) populations of two-state systems, which have a maximum amount ...
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1k views

canonical and microcanonical ensemble

What does one mean by canonical and micro canonical ensemble in statistical mechanics? Can one elaborate on this in a very simple way with examples? Pardon me, if it is a very simple thing; I am a ...
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4answers
695 views

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 ...
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134 views

Hydrostatic forces in a bowl of cereal [duplicate]

This morning I was eating cereal which consisted of roughly spherical pieces just shy of one centimeter in diameter. By the time I was nearly finished, the cereal pieces were floating in a monolayer ...
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1answer
169 views

How hot is your photon?

This question comes from my answer to the question Can a cubic meter of space at absolute zero have any object with mass inside? and the related discussion under it. To summarize, I stated that the ...
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2answers
286 views

Ising model observables

Is there a formula or equation relating $\langle E\rangle$ and $\langle M\rangle$ (average spin per site) and $\langle E^2\rangle$ to temperature $T$ for the square lattice Ising model at zero ...
5
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1answer
195 views

Energy fluctuations in quantum canonical ensemble

How would you go about showing that in the quantum canonical ensemble (that is, in the density matrix and operator formulation), the energy fluctuations, namely $\langle H^2\rangle - \langle ...
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334 views

The critical point of Bose-Hubbard model

The Hamiltonian of Bose-Hubbard model reads as $$H=-t\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1)-\mu\sum\limits_in_i$$. In the limit $t\ll U$, the ground ...
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1k views

The analogy between temperature and imaginary time

There are many statements about the relation between time and temperature in statistical physics and quantum field theory, the basic idea is to interpret (inverse) temperature in statistics as "time" ...
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1answer
479 views

Ideal gas and diatomic gas with same temperature

If a box of ideal gas and another box of diatomic gas are in thermal equilibrium, does it mean that the average translational energy of ideal gas particle (A) is the same as that of diatomic gas ...
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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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347 views

Proof that Statistical Mechanics is a model of Themodynamics

The laws of thermodynamics are essentially four axioms of a mathematical theory. The expectation values of a statistical ensemble are supposed to satisfy the axioms of thermodynamics (under the ...
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1answer
138 views

Why is it difficult to mix helium and nitrogen gases?

I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for ...
5
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1answer
107 views

Does it make sense to define the mean free path in quantum mechanics?

The mean free path defined in classical molecule dynamics has a strong classical flavor. Is it sensible to generalize the idea to quantum mechanics?
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186 views

What is the phenomenological logic behind Fermi liquid theory

I am a super beginner when it comes to Solid State Physics and when wanting to learn more on the subject, I end up reading on Landau's Fermi liquid theory that supposedly justifies the quasi-free ...
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319 views

A thermodynamic transformation that can be represented by a continuous quasistatic path in its state space may still be irreversible. Why?

A thermodynamic transformation that has a path (in its state space) that lies on the surface of its equation of state (e.g., $PV=NkT$) is always reversible (right?). However, if the path is a ...
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321 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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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: ...
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71 views

Why $\epsilon > \mu$ for Bose-Einstein distribution (but not for Fermi-Dirac)?

For fermions $$\bar{n}_{FD}=\frac{1}{e^{(\epsilon -\mu)/kT}+1}$$ and $\epsilon$ can be bigger or small than $\mu$. However, for bosons: $$\bar{n}_{BE}=\frac{1}{e^{(\epsilon -\mu)/kT}-1}$$ which ...
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125 views

Is temperature discrete

Because an object's temperature is inversely proportional to the wavelength of blackbody radiation which it emits, physicists have theorized the existence of Planck temperature at around $1.4×10^{32}$ ...
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713 views

Grand canonical partition functions for Bose-Einstein statistics vs. Maxwell-Boltzmann statistics

In Bose-Einstein statistics, the grand canonical partition function is $$\mathcal{Z}=1+e^{-\beta(\epsilon-\mu)}+e^{-2\beta(\epsilon-\mu)}+e^{-3\beta(\epsilon-\mu)}+\cdots$$ In Maxwell-Boltzmann ...
5
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1answer
113 views

Do we have a fundamental Hamiltonian for the system of H$_2$O molecules?

From the quantum mechanics(QM) viewpoint, does there exist a Hamiltonian $H$ for the system of H$_2$O molecules? Assume that the number of H$_2$O molecules is fixed. Imagine that by calculating the ...
5
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1answer
213 views

Topological Phases and Confinement

I recently attended a talk in which the speaker defined a topological phase as "A phase which has a gap above the ground state for bulk excitations in the thermodynamic limit." I am interested in what ...
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425 views

What would happen if energy was conserved but phase space volume wasn't? (and vice-versa)

I'm trying to understand the relationship between the two conservation laws. As I understand, Liouville's result is a weaker condition: it relies merely on the particular form assumed by Hamilton's ...
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319 views

The strong Markov property of Gibbs measures in 2D Ising Model

My background is that of a mathematician. I have a question about the two Dimensional Ising Model. I think the terminology I use is similar to the physical. I'm trying to understand the following ...
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2answers
169 views

Pair interactions on finite square lattice

I am looking for an exact or approximate solution to a statistical lattice-particle problem: Given a lattice of size $L\times L$ where $\rho\cdot L^2$ particles are randomly distributed, calculate ...
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2answers
413 views

What physical processes may underly the collisional term in the Boltzmann equation, and how do they increase entropy?

Consider particles interacting only by long-range (inverse square law) forces, either attractive or repulsive. I am comfortable with the idea that their behavior may be described by the collsionless ...
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62 views

Vanishing Planets?

If we put a solid sphere in space, it will lose some molecules which will form a sort of an atmosphere around it so that we have the required vapour pressure for solid-vapour equilibrium (Temp. of ...
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151 views

In thermodynamic systems why must the free energy of the system be minimized?

Is this somehow a consequence of the second law of thermodynamics?
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335 views

Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution

Maxwell derived the shape of the probability distribution of velocity of gas particles by starting with just two assumptions. These are: The probability distribution is rotation invariant. The ...