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

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75 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
votes
3answers
970 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
1k 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
votes
1answer
400 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 ...
3
votes
4answers
2k 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 ...
1
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0answers
181 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 ...
4
votes
1answer
308 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
votes
2answers
433 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 ...
15
votes
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. Transcription: ...
4
votes
1answer
802 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 ...
0
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2answers
584 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
votes
1answer
380 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 ...
1
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0answers
47 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
1k 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
votes
1answer
123 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 ...
9
votes
1answer
453 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 ...
2
votes
3answers
934 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 ...
13
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6answers
2k views

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
votes
1answer
403 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
votes
1answer
302 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.
-2
votes
2answers
338 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 ...
5
votes
3answers
621 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 ...
4
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1answer
307 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 ...
2
votes
3answers
240 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 ...
5
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0answers
365 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 ...
3
votes
1answer
261 views

From spectrum/dispersion relation to the partition function

I know the spectrum/dispersion relation for a bosonic system. $$E \left( \mathbf{k} \right) = \cdots$$ Is there a general method for writing down the partition function when the spectrum of the ...
7
votes
0answers
312 views

Information geometry of 1D Ising model in complex magnetic field regime

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
6
votes
2answers
298 views

Renyi entropy in physical systems

We know that the Shannon entropy $H(P)=- k_{\mathrm{B}}\sum_i p_i \ln p_i$ is mostly the entropy of the thermodynamic systems. Does the Renyi measure $H_{\alpha}(P)=\frac{1}{1-\alpha}\log \sum ...
6
votes
1answer
354 views

What is the information geometry of 1D Ising model for a complex magnetic field?

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
4
votes
2answers
1k views

Can a system entirely of photons be a Bose-Einsten condensate?

Background: In Bose-Einstein stats the quantum concentration $N_q$ (particles per volume) is proportional to the total mass M of the system: $$ N_q = (M k T/2 \pi \hbar^2)^{3/2} $$ where k ...
1
vote
2answers
320 views

Polarisation directions in standing waves in cubical cavity

I was studying Rayleigh-Jean's formula. The author has assumed a cubical cavity of each side $L$ with perfectly reflecting surfaces. According to author, there are two perpendicular directions of ...
8
votes
5answers
5k views

Why was the universe in a 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 ...
8
votes
2answers
6k views

How to derive Fermi-Dirac and Bose-Einstein distribution using canonical ensemble?

My textbook says that microcanonical ensemble, canonical ensemble and grand canonical ensemble are essentially equivalent under thermodynamic limit. It also derives Fermi-Dirac and Bose-Einstein ...
4
votes
3answers
2k views

How to understand temperatures of different degrees of freedom?

So I'm reading this book, where after the preface and before the models there is a section called General Notions and Essential Quantities, which introduce some things I don't understand. They regard ...
1
vote
2answers
251 views

Reconstruction of information stored in an evaporating black hole from the emission spectrum?

For simple setups, where the radiation field deviates not too far from thermodynamic equilibrium (< 10 %), corrections to the Planckian thermal emission spectrum can be calculated (and measured) ...
9
votes
1answer
82 views

Renyi fractal dimension $D_q$ for non-trivial $q$

For a probability distribution $P$, Renyi fractal dimension is defined as $$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$ where $R_q$ is Renyi entropy of order $q$ ...
7
votes
5answers
485 views

Theoretical proof forbidding Loschmidt reversal?

In a famous debate, Loschmidt criticized Boltzmann's new theory of statistical mechanics by asking what would happen if the velocities of all the atoms were reversed. Typical objections are that such ...
1
vote
1answer
287 views

Numerical algorithms to generate a random wavefunction from a thermal ensemble

I am seeking an algorithm to generate a random wavefunction = $\sum {c_i |\varphi _i\rangle }$ from a thermal ensemble, whose density matrix $\rho \sim e^{-\beta H}$, without the need to diagonalize ...
10
votes
0answers
89 views

Quantum statistics of branes

Quantum statistics of particles (bosons, fermions, anyons) arises due to the possible topologies of curves in D-dimensional spacetime winding around each other What happens if we replace particles by ...
2
votes
1answer
170 views

Renormalization Group for anisotropic “Gaussian” model

I'm considering an "anisotropic" Hamiltonian of the form $$\beta H = \int d^n r_{||} d^{d-n} r_{\bot} \frac{K}{2} (\nabla_{||} m)^2 + \frac{L}{2} (\nabla^2_\bot m)^2 + \frac{t}{2}m^2 - hm$$ which in ...
4
votes
1answer
371 views

Renormalization Group: Different fixed points

Extending the Gaussian model by introducing a second field and coupling it to the other field, I consider the Hamiltonian $$\beta H = \frac{1}{(2\pi)^d} \int_0^\Lambda d^d q \frac{t + Kq^2}{2} ...
1
vote
2answers
283 views

RG of the Gaussian Model: Finding the scaling factor

I'm studying how the Renormalization Group treatment of the simple Gaussian model, $$\beta H = \int d^d r \left[ \frac{t}{2} m^2(r) + \frac{K}{2}|\nabla m|^2 - hm(r)\right]$$ In momentum space, the ...
1
vote
2answers
516 views

How do derive this result in stat-mech style

I'm going through (well, at least I'm planning to) Rief's book about statistical mechanic (I want to improve my knowledge). I want to be serious about this so I'm trying to solve as much problem as I ...
5
votes
3answers
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 ...
1
vote
1answer
154 views

On BE and FD Statistics

Lets consider the Bose-Einstein and Fermi-Dirac statistics: Bose-Einstein statistics: $$\langle n_i\rangle = \frac{1}{\exp{[(\epsilon_i-\mu)/kT]} - 1}$$ Fermi-Dirac statistics: $$\langle ...
6
votes
1answer
426 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 ...
3
votes
1answer
135 views

Definition regarding percolation

in a homework sheet studying bond-percolation on the Bethe lattice, a function $g(r)$ is introduced as "the probability of finding two nodes separated by a distance $r$ on the same cluster". Now ...
4
votes
1answer
949 views

Calculating the heat capacity of a system

I have started reading Statistical Physics by F. Mandl and I would appreciate some help with the following exercise A system consists of $N$ weakly interacting subsystems. Each subsystem possesses ...
2
votes
3answers
611 views

Should annealed disorder be characterized by the average of the partition function?

Most of the literature says that for a quenched average over disorder, an average over the log of the partition function must be taken: \begin{equation} \langle \log Z \rangle, \end{equation} while ...
6
votes
4answers
1k views

Partition Function as characteristic function of energy?

I'm going through a book on statistical mechanics and there it says that the partition function $$Z = \sum_{\mu_S} e^{-\beta H(\mu_S)}$$ where $\mu_S$ denotes a microstate of the system and $H(\mu_S)$ ...