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

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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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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 ...
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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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199 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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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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223 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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279 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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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
852 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
339 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 ...
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406 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 ...
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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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786 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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330 views

What is the resolution to Gibb's paradox?

This question is essentially a duplicate of Gibbs Paradox - why should the change in entropy be zero?. The question concerns the following situation: I have some gas of identical particles and they ...
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4answers
687 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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1answer
127 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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159 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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285 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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187 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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1answer
332 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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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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468 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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121 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 ...
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104 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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183 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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1answer
316 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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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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70 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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123 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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705 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 ...
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1answer
112 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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211 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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415 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 ...
5
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1answer
317 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
411 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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147 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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328 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 ...
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166 views

What information is lost in the symmetrization necessary to derive the BBGKY hierarchy?

The book on Kinetic theory I'm reading derives the BBGKY hierarchy after introducing the reduced distribution functions $f_s(q^1,p_1,q^2,p_2,\dots,q^s,p_s):=\int\ \rho\ \ \mathrm d q^{s+1} \mathrm d ...
5
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1answer
82 views

Meaning of the 'deep lattice limit' and 'shallow lattice limit'?

In condensed matter literature, at many places, the phrase 'deep lattice limit' is used. Please tell what is the deep lattice limit and the shallow lattice limit?
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1answer
459 views

Mean-field theory and spatial correlations in statistical physics

In statistical physics, mean-field theory (MFT) is often introduced by working out the Ising model and it's properties. From a spin model point of view, the mean-field approximation is given by ...
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230 views

Are isolated many-particle quantum systems always in a pure state?

I am trying to understand pure and mixed states better. If I have N quantum particles in an isolated system. The many-particle state is a superposition of the product of single-particle states by the ...
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592 views

Percolation in a 2D Ising model

For a 2D Ising model with zero applied field, it seems logical to me that the phases above and below T_c will have different percolation behaviour. I would expect that percolation occurs (and hence ...
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320 views

What is the mathematics behind artificially generated plasmas via electric fields?

The ionization degree of a plasma is given by the Saha equation, which depends on the temperature and the particle specific ionization energy. In thermal equilibrium, the relation between ionization ...