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

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Gibbs Paradox - why should the change in entropy be zero?

The Gibbs paradox deals with the fact that for an ideal gas with $N$ molecules in a volume $V$ seperated by a diaphragm into two subvolumes $V_1,V_2$ with $N_1,N_2$ particles in each subvolume, ...
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182 views

Dependence of chemical potential to zero point of energy

The chemical potential is defined as: $$ \mu = -T\frac{\partial{S(N,V,E)}}{\partial{N}} $$ It seems to me that this is completely independent of where I put the reference point of energy, because only ...
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Bohr-van Leeuwen theorem and quantum mechanics

Preamble: If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
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670 views

Analogue of Princeton Companion to Mathematics for Physics?

I would like to know if there are compendiums much like the Princeton Companion to Mathematics for physics (especially classical physics: fluid mechanics, elasticity theory, Hamiltonian formalism of ...
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259 views

Why do phase transitions even exist? Why not smooth density change curves?

Why do phase transitions even exist? Why not smooth density change curves? What properties of matter, quantum or otherwise, predicts that matter will undergo phases at different pressures and ...
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Why is the Gibbs Free Energy $F-HM$?

With magnetism, the Gibbs Free Energy is $F-HM$, where $F$ is the Helmholtz Free Energy, $H$ is the auxiliary magnetic field, and $M$ is magnetization. Why is this? Normally, in thermodynamics, we ...
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331 views

Why Landau Level quantization is observed only in low temperature and strong magnetic field in real experiment?

I know that Quantum Hall Effect and Fractional Quantum Hall Effect origin from Landau Level quantization. In magnetic field, the energy of in-plane(plane perpendicular to magnetic field) degree of ...
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373 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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The definition of Density of States

The density of states (DOS) is generally defined as $D(E)=\frac{d\Omega(E)}{dE}$, where $\Omega(E)$ is the number of states. But why DOS can also be defined using delta function, as ...
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458 views

Motivation for maximum Renyi/Tsallis entropy

The Conditional limit theorem of Van Campenhout and Cover gives a physical reason for maximizing (Shannon) entropy. Nowadays, in statistical mechanics, people talk about maximum Renyi/Tsallis entropy ...
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How can the microstates be measured with zero energy expenditure?

James P. Sethna. Statistical Mechanics. Exercise 5.2: What prevents a Maxwellian demon from using an atom in an unknown state to extract work? The demon must first measure which side of the ...
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176 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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Is there a formal definition of a macroscopic variable in statistical mechanics?

Intuitively it's easy to accept that the usual variables like temperature, internal energy, etc. are 'macroscopic', but does there exist a formal definition of a macroscopic variable? In other ...
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188 views

Why are large scale structures isotropic in the Ising model?

I have at least a qualitative understanding of why the critical state of the Ising model is scale invariant, by arguments to do with renormalisation, which I understand only very roughly. However, in ...
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3answers
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Does entropy have a physical meaning?

Entropy is incredibly useful as a mathematical tool. But what does it actually mean? I understand that the Boltzmann entropy is defined by: $$S=k\ln{\Omega}$$ With $\Omega$ being the multiplicity ...
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4k views

Is there a phase transition between a gas and plasma?

Does a phase transition occur as a gas is heated to create a plasma? If so, is this a first or second order phase transition? Also, does the presence of a phase transition depend on the pressure or ...
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706 views

``What is life?'' by a physicist definition [closed]

The question is about defining ``What is life?'' in the field of Physics. Whether there is any (insightful) way of defining ``What is life?'' from physicists. There are pioneer works, including ...
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1answer
258 views

Is it always possible to express an operator in terms of creation/annihilation operators?

I'm referring to "Path integral approach to birth-death processes on a lattice", L. Peliti, J. Physique 46, 1469-1483 (1985), available at: http://people.na.infn.it/~peliti/path.pdf The article is ...
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676 views

Axiomatic statistical mechanics

Ive read a few courses on statistical mechanics, and while their textual explanations and example choices differ, the flow of information from microscopy to macroscopy seems the same, and reading ...
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953 views

Surface tension of solutions and mixtures

The inspiration for this question is over on cooking.stackexchange, asking more about actual measurements for commonly consumed liquids, but I'm interested more generally as well. What determines the ...
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Why does warm water sink?

It is well known that water at 4C is denser than water at 0C. This is the usual explanation for why a body of water freezes from the surface (also it's because ice is even less dense, but that's ...
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204 views

Does a vacuum, suddenly opened, become hotter than its surroundings?

Suppose you have an insulated container that is equipped with a valve to let air in. Initially the container is evacuated. You then quickly open the valve, allowing air to rush in. What is the ...
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262 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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What is an intuitive explantion for the fact that the Maxwell-Boltzmann distribution of energies is independent of mass?

If you take the Maxwell-Boltzmann distribution of velocities (which depends on the mass) and substitute $v=\sqrt{\frac{2E}{m}}$ you get the distribution for the energies, which turns out to be ...
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81 views

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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343 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 ...
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370 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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232 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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Obtaining the canonical distribution from Fokker-Planck equation?

First I will provide a summary of the problem. Subsequently, I will provide more detail regarding the problem. Please note that entropy is in units of the Boltzmann constant. Summary I have a ...
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197 views

Simple estimation of the critical temperature of water

I'm trying to develop fermi estimation skills and I came up with a question for which I don't even know where to start from. Here goes: Is it possible to estimate the critical temperature (say in ...
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148 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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624 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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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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250 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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135 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 ...
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418 views

Stability of the vacuum state of interacting quantum fields

"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
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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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Are the physical laws scale-dependent?

If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study? As an ...
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677 views

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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What is the general statistical definition of temperature?

Temperature in an isolated system is defined as: $$\frac{1}{T} = -\frac{\partial{S(E,V,N)}}{\partial{E}} $$ But I wonder how one can generalize this to a random system. Or for instance to a point in ...
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663 views

Temperature; Why A Fundamental Quantity?

Temperature is just an indication of the combined property of mass of the molecules and their random motion. We can explain no effective energy transfer between two conducting solid bodies in contact ...
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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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982 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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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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834 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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1answer
366 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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1answer
166 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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What does third law of thermodynamics tell us?

I just have a question concerning the third law of thermodynamics. The third law describes that the entropy should be a well defined constant if the system reaches the ground state which depends ...
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Chemical potential of a Bose gas

In my course, there is this fact : In a Bose gas, the chemical potential $\mu$ must always be lower than the smaller level of energy $\epsilon_0$. I find this strange, because if we put a Bose ...
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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 ...