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

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upper critical dimension in field theory

Is there field theory which describe a second order phase transition without upper critical dimension ? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.
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1answer
419 views

Relation between external magnetic field intensity H, magnetisation M and the entropy?

How are the external magnetic field intensity H, magnetisation M and the entropy related to each other? i.e. if I change the magnetic field intensity by dH what will be the change in entropy dS in ...
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1answer
149 views

Thermodynamics and cross entropy

I am facing with the concept of cross entropy. I would like to know the thermodynamic and statistical meaning of cross entropy (if exists)?
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1answer
930 views

Autocorrelation Functions <---> Pair Correlation Functions

Are there any ways to convert an autocorrelation function to a pair correlation function, and vice versa?
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2answers
190 views

Physical Significance for Duality Formula for Entropy

I am studying quantum statistical mechanics from the mathematician's perspective. I don't quite understand what the duality formula for entropy is really saying (or why there is a "duality"). If $A$ ...
3
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3answers
362 views

Power laws and deterministic systems

I am facing the following question. It is well known that power laws arise in many situations in nature. They arise even in thats physical systems that are completely deterministic (e.g. sand piles). ...
2
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1answer
214 views

Equivalent system in Centre manifold theory

I was studying the centre manifold theory. It says (see Kuznetsov page 155, theorem 5.2) that the system on the left side of the picture is topologically equivalent to the one on the right. $ ...
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2answers
280 views

What's the classical limit of the pressure of the ultrarelativistic Bose gas

The pressure for the ultrarelativistic Bose gas is $$p~=~U/(3V) ~\propto~ (kT)^4/(hc)^3.$$ It looks to me like it diverges for $h \to 0$. Looking at the derivation, it diverges because $h$ is the ...
2
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1answer
76 views

Is there an abstract notion of heat within a microscopical system?

The microstates of a system are said to be unobservable. I can introduce the entropy as a measure of the number of microstates, which lead to the same macroscopic variables. So in this detailed ...
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1answer
249 views

Black body balloon in vacuum [closed]

The problem statement, all variables and given/known data There is a perfectly spherical balloon with surface painted black. It is placed in a perfect vacuum. It is gently inflated with an ideal ...
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2answers
340 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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2answers
138 views

Is ground energy of interacting fermions always higher that that of bosons?

Consider two systems, each made of $N$ particles. In both systems particles interact pairwise and the interaction is given by the same Hamiltonian for both systems. Any other constraints and/or ...
2
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0answers
78 views

Factorization of fermionic scattering integral in 2d momentum rep

the scattering integrals for fermions involves both momentum ($k$) and energy ($k^2$) conservation and a nonlinear phase space factor of a distribution function $f(k)$. $$\begin{multline}I(k) = ...
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4answers
907 views

Ignorance in statistical mechanics

Consider this penny on my desc. It is a particular piece of metal, well described by statistical mechanics, which assigns to it a state, namely the density matrix $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
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3answers
2k views

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 ...
8
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7answers
665 views

How does such strange microscopic behavior at the atomic level (quantum mechanics) lead to the macroscopic behavior at our level?

So, I'm only a high school student researching quantum physics, and I find it very interesting. However, there's one question that keeps nagging at me in the back of my head. How exactly do odd ...
8
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0answers
145 views

Measure of Lee-Yang zeros

Consider a statistical mechanical system (say the 1D Ising model) on a finite lattice of size $N$, and call the corresponding partition function (as a function of, say, real temperature and real ...
4
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1answer
253 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 ...
2
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1answer
534 views

How specifically do emulsifiers work?

I'd like to understand better how emulsifiers prevent droplet coalescence. There must be something more they do than just lower the surface tension between the droplet and the ambient substance. I ...
2
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1answer
181 views

Quantum Stat-Mech Proof of an Inequality for the Partition Function

I have the following problem that I was unable to solve for class, but I had a couple first steps that I started with that I am unable to finish. I know I can't get this since it's already been ...
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2answers
146 views

Discussions of the axioms of AQFT

The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, ...
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1answer
115 views

What's the meaning of the coupling change after a renormalization (in the 1-dim Ising Model)?

What does it mean that after the theory (1-dim Ising model here, but the question is general) is renormalized one time and $g_i\rightarrow g_i'$, that the couplings are weaker, even if the theory ...
8
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1answer
169 views

Do thermodynamic quantities in CFT correspond to something different in AdS/CFT?

From what I've (hopefully) understood from the AdS/CFT correspondence, physical quantities have a dual version. For example, the position in the bulk is the scale size (in renormalization), and waves ...
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0answers
193 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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5answers
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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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0answers
67 views

Do bipartite spin glasses have simple relaxation dynamics?

From what I gather, a Boltzmann machine (BM) is essentially a spin glass with no applied field evolving under Glauber dynamics (if this is at all mistaken, I don't think it will be off enough to ...
6
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3answers
826 views

What is the relationship between Schrödinger equation and Boltzmann equation?

The Schrödinger equation in its variants for many particle systems gives the full time evolution of the system. Likewise, the Boltzmann equation is often the starting point in classical gas dynamics. ...
6
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1answer
734 views

The equipartition theorem in momentum space

Motivated by the answers to this question on turbulence, I'm interested in an explanation and/or derivation/reference of the equipartition theorem in momentum space. To formulate it as a question: ...
6
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1answer
307 views

Thermodynamic limit “vs” the method of steepest descent

Let me use this lecture note as the reference. I would like to know how in the above the expression (14) was obtained from expression (12). In some sense it makes intuitive sense but I would ...
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4answers
1k views

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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0answers
120 views

Does the spin glass corresponding to a restricted Boltzmann machine have a characteristic timescale?

From what I gather, a Boltzmann machine can be identified with a spin glass. Though I don't know the details yet (and would welcome any references within the last 5 years--not, e.g. MacKay, etc.), I ...
3
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1answer
238 views

Scaling with the Ising Model

I am stuck with one formula in the CFT book by Di Francesco and al. Chapter 3. Equation 3.46 third step, for those who don't have the book, he integrates out degrees of freedom from the Ising Model by ...
6
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2answers
373 views

Statistical Mechanics treatment of the reaction process?

I'm searching for an at least semi-rigorous Statistical Mechanics description/treatment of a (spatially resolved) chemical reaction process of a macroscopic portion of at least two different species ...
13
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4answers
3k views

What does Peter Parkers formula represent?

Okay, so the trailer for the new Spider Man movie is out and appearently our friendly physicist from the neightborhood came up with something. However I can't find out what this is. ...
4
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1answer
655 views

Energy per particle vs. chemical potential vs. evaporation energy

There is a system of N particles. They interact and are bound together with a binding energy Eb (or potential energy). To characterize the system there are multiple terms Energy per particle Eb(N)/N ...
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2answers
451 views

Statistical interpretation of Entropy

I'm preparing my statistical physics course, and while writing the lecture notes it says that a system with non distinguishable particles has much less microstates asociated with a particular ...
2
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1answer
341 views

Joining the definitions of entropy

$\int \frac{Q_{rev}}{T} = \Delta(k_B\ln\Omega)=\Delta S$ Could anyone give some definite proof for this? I was able to prove that the two definitions of change in entropy are equivalent for an ...
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0answers
44 views

Negative chemical potential [duplicate]

Possible Duplicate: Chemical potential The chemical potential of electron and positron is equal but with opposite sign. How one can visualize the negative chemical potential of positron, ...
0
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1answer
679 views

Deriving an Expression for Entropy

How to derive an expression for entropy in form of $S = \ln \Omega$ from the form $\displaystyle{S = - \sum_i \; p_i \ln p_i}$ ? That is the last formula taken as a definition of entropy. Just a ...
3
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1answer
116 views

Random bond Ising model and computational efficiency

If you want to find the ground state of the 2d random bond Ising model (no field), a computationally efficient algorithm exists to do it for you (based on minimum weight perfect matching). What about ...
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1answer
352 views

Reduced density matrices for free fermions are thermal

Many recent papers study entanglement in eigenstates of fermionic free hamiltonians (normally on a lattice) using the basic assumption that the reduced density matrices are thermal (e.g. Peschel ...
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3answers
594 views

Definition of Fluctuations and Perturbations

The terms fluctuations and perturbations are frequently used in physics with different meanings. But they are confusing. Both terms seems to be same. Is there any one who can explain lucidly these ...
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6answers
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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 ...
2
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1answer
337 views

How to choose the right units to compute the phase space volume in classical statistical mechanics?

Without the natural unit $\hbar$, why doesn't it seem to be a problem for Statistical Physics to define $$S=k_B\ log(\Omega)\ ?$$ If $\Omega$ is given in one unit system and I switch to other units ...
2
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1answer
230 views

Infinite quantum well width $L$ to $2L$ adiabatic process

If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
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2answers
320 views

Occam's razor on spin statistics theorem?

Highly related to A reading list to build up to the spin statistics theorem I see 2 parts to the spin statistics theorem: (spin $n$ or $n+\frac{1}{2}$) step 1 given that a spin is integral or ...
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2answers
503 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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1answer
294 views

What are conditions for the existence of a critical value (for a phase transition)?

Can there only be a critical temperature if there is some natural unit for an observable in the model, i.e. if there is a natural scale for something? Otherwise I don't see how for a system there ...
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3answers
226 views

How to “read” the temperature of an abstract system?

How can I interpret the parameter temperature $T$, if I'm not given the description of the system in terms of the equation of state, $E(S,V\ )$ or $S(E,V\ )$ and so on. In many systems it makes sense ...
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265 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 ...