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

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6
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1answer
810 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 ...
3
votes
1answer
47 views

If Black holes are maximal entropy how can they evaporate?

According to Hawking/Bekenstein a black hole represents the highest amount of entropy for a given volume, (actually the entropy is related to the surface area of the black hole but the fact that they ...
-2
votes
2answers
59 views

Entropy always increases in a closed system - what if the universe is open?

An interesting question I was asked: Entropy always increases in a closed system - what if the universe is open? Does that mean that entropy can decrease in such a system? Of course, I think there is ...
0
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0answers
13 views

Rugged Energy Landcapes (Free Energy vs Potential Energy Questions)

A spin glass has what is called a "rugged energy landscape." That is, when you cool down below a certain temperature, the system divides into many wells, all corresponding to slightly different ...
0
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0answers
20 views

Rogers-Ramanujan and integrable systems

I'd like to understand the underlying geometry of the Rogers-Ramanujan continued fraction from the point of view of integrable systems (ideally Toda type theories). The generating function ...
1
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1answer
63 views

Operator formalism in QFT in Euclidean space-time

In QFT there are two very useful general approaches to study quantum fields (on the Minkowski space-time): path integrals and operator formalism. Sometimes they give the same results, sometimes one ...
-1
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1answer
54 views

Deriving Ideal Gas law from Hamiltonian Mechanics

I just don't understand the explanation in Wikipedia. Is there a nice & elegant way of arriving at the Ideal Gas Law from Hamilton's Equations?
0
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0answers
28 views

How do inverse of Kirchoff matrix of a polymer possess the information for its mobility?

In Normal Mode Analysis of polymers like proteins, I have seen that mobility (measures like root mean squared fluctuations) can be found from the eigen values and eigen vectors of inverse of Kirchoff ...
0
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1answer
68 views

Thermal average, thermal fluctuations

I've a doubt concerning the physical meaning of "thermal average" and the "thermal fluctuation" in the canonical ensemble. Let's consider a very simple thermodynamic system: N particles, at fixed ...
4
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3answers
56 views

Why do Temperatures Equalize

I have some Oxygen at Temp A in one container and some Nitrogen at Temp B in another container. If I mix these two containers eventually both the Oxygen and Nitrogen will be at the same temperature. ...
1
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3answers
46 views

When does the Boltzmann distribution apply?

What are the requirements for a system to be described by the Boltzmann distribution in equilibrium? For example, should all the particles be identical? No attractors in the phase space? ...
21
votes
1answer
305 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each ...
-3
votes
1answer
37 views

Entropy for $N$ number of particles [on hold]

If there are $N$ number of non-interacting and distinguishable particles which have either Energy $E_1$ or $E_2$ , then a. What will be the entropy $S(n)$ for such system? ($n$ is the number ...
0
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0answers
18 views

Construct recurrence relation for the temporal evolution of a Master equation

Say that we have a system evolving over discrete timesteps. The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a ...
1
vote
0answers
23 views

Extensiveness of entropy in classical microcanonical ensemble

In introducing microcanonical ensemble of classical statistical mechanics one pretty much starts by postulating that entropy of the system has the form $S(V,E) = k \log \Gamma(V,E)$, where $\Gamma$ ...
0
votes
1answer
48 views

A conceptual question related to statistical mechanics

Statistical mechanics allows us to consider an ensemble of systems, each of which consisting of only a single particle. Once we write the partition function for the system of one particle, we can ...
0
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0answers
22 views

Spread of gases in a room

I have had some thermodynamics and statistical mechanics, but I don't know much fluid mechanics. I am not sure how to model the spread of gases in a room in the case of a fire or some leaking vent. ...
0
votes
1answer
35 views

White noise in the Langevin model and it's autocorrelation function

I am having some trouble understanding and interpreting the noise term in the Langevin equation for a colloidal particle in a fluid. By the Langevin model, I mean the following model as the equation ...
5
votes
1answer
1k views

Infinite-range 1D Ising model + Hubbard-Stratonovich-Transformation

I have a probably quite simple question RE the HST. After some work, I obtain as the partition function for the infinite range 1D Ising model $$Z = \int_{-\infty}^\infty \frac{dy}{\sqrt{2\pi / ...
0
votes
0answers
40 views

Calculation of charged sphere distribution near a wall in Cartesian coordinates

I am following a similar derivation as found in the beginning of this paper "Quantitative aspects of the growth of (charged) silica spheres" by A.P. Philipse. This paper calculates the growth of a ...
8
votes
3answers
112 views

Gross “temperature” of a globular cluster

Globular clusters can be very large, which means we can do statistics about the stars in them. And that means we can try matching their star-as-particle potential/kinetic energy distribution against ...
1
vote
1answer
48 views

Two definitions of the density matrix?

There seems to be two different definitions of definitions of density matrices in Physics. In Quantum Information we define a the density matrix associated with a wave function $ | \psi \rangle$ as ...
3
votes
1answer
116 views

Density of states and anisotropic distribution functions

We consider a $3D$ dynamical system. Its distribution function is given by the function ${ (\mathbf{x},\mathbf{v}) \mapsto f (\mathbf{x},\mathbf{v})}$, so that $$ \mathrm{d}^{3} \mathbf{x} \, ...
1
vote
0answers
44 views

Can the second law of thermodynamics be violated in a small enough system if tried repeatedly enough?

Second law of thermodynamics is observed in the universe because statistics favors it, right? And in large enough system this statistical tendency becomes certainty. Does it also mean that negative ...
1
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1answer
107 views

Molecular dynamics and detailed balance

In developing methods to perform Monte Carlo simulations one sufficient condition to preserve the stationarity of the target probability distribution is to impose detailed balance i.e. [Gardiner page ...
3
votes
0answers
79 views

Understanding various types of motion

In classical statistical mechanics, given a system of particles, one often goes about classifying various dynamics (or types of motion) the system may exhibit on different time scales, but studying ...
0
votes
1answer
22 views

Why use dimensionless heat capacity?

Perhaps this is blindly obvious, but in typical discussions of statistical mechanics (with, say, constant volume) one often finds that, rather than using the heat capacity $$ C_V = \frac{\partial ...
1
vote
1answer
35 views

Adiabatic transition from superfluid to Mott insulator?

I have a question about the dynamical passage from superfluid to Mott insulator state in the Bose-Hubbard model. Is it possible to go from superfluid region to the Mott insulator by changing the ...
9
votes
4answers
216 views

What is the real cause of the boiling (forming of bubbles) of water?

I've got a question about the boiling of water. I'm a first year physics student and from the Netherlands. I've searched alot about the boiling of water and this confused me. Everyone said something ...
0
votes
0answers
24 views

How to interpret two distinguishable particles with N possible states?

NOTE: Please do not provide an answer to the questions. If I am incorrect, please explain why, and if I am correct, please try to further my understanding. I think that this is a constructive way to ...
4
votes
1answer
64 views

A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
3
votes
1answer
53 views

Is the principle of indifference enough to derive the microcanonical ensemble?

The microcanonical ensemble is usual motivated solely by the principle of indifference. Textbooks usually say something along the lines of "If the only thing we know about a system is its total ...
4
votes
3answers
415 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
2
votes
1answer
59 views

Hamiltonian or free energy corresponding to 2+1D Kuramoto-Sivashinsky model

I am trying to understand if the deterministic 2+1D Kuramoto-Sivashinsky equation $$ \partial_t h = -\nu \nabla^2 h - K \nabla^4 h + \frac{\lambda}{2} (\nabla h)^2, $$ where $\nu$, $K$, $\lambda$ ...
0
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0answers
46 views

Connection between statistical and quantum mechanics

I am aware of Gibbs measures, given the energy (Hamiltonian) of an arrangement, one can determine the frequency of the arrangement. Plug the energy level in the Boltzman equation and there you go. I ...
5
votes
4answers
374 views

Why is entropy an extensive quantity?

If we have two identical isolated macroscopic systems both with energy $E$. The number of accessible states of each of them is $\Omega(E)$ and hence the entropy is $\ln\Omega(E)$. Now if we put them ...
0
votes
0answers
32 views

Is the equipartition theorem derivable from more basic principles [duplicate]

Is the equipartition theorem really a theorem and derivable from more basic assumptions or is it just a hypothesis. Some of the ways energy is partition is not to squared quantum numbers (e.g. ...
1
vote
1answer
31 views

What is the word describing the pairs: temperature and energy, chemical potential and particle number?

I keep forgetting the word describing the pairs of coupled quantities in stat. mech. e.g. inverse temperature $\beta$ and internal energy $E$ or chemical potential $\mu$ and particle number $N$. I ...
1
vote
1answer
134 views

How does the Lennard Jones Potential changes for interaction between particles of different sizes?

I am interested in incorporating a Lennard-Jones potential in a simulation. When the interaction only involves the same type of particle, with same characteristics, we can use reduced units, scaling ...
0
votes
1answer
128 views

Thermodynamic transformation

Why it is so that any reversible thermodynamic transformation is quasi- static ? Also, Why the converge is not necessarily true ?
2
votes
3answers
234 views

Entropy change in an irreversible process between 2 equilibrium state

Calculating entropy change in an irreversible process between 2 states requires computing the change in entropy for any reversible process between the 2 same states, but why? If someone could provide ...
0
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0answers
18 views

Gradient effects in continuum mechanics

What I have learned is that inhomogenous materials (materials with different material properties over space and time) can be treated by the homogenization technique ...
-1
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0answers
17 views

Why does the Stefan-Boltzmann law work for power absorbed?

The setup is as follows: There is a body of emissivity $e$ and surface temperature $T$ whose surroundings have a temperature $T_s$ and may be assumed to be a black body. The body radiates at a ...
0
votes
1answer
39 views

Conservation of energy and realm of possibility

The law of conservation of energy states that energy cannot be created or destroyed. Based on this principle, you can safely conclude that any effect resulting from a cause must somehow keep all ...
5
votes
1answer
82 views

How to justify the entropy maximum postulate using Statistical Mechanics?

The entropy maximum postulate states that given a thermodynamic system there's a function $S$ of the extensive parameters called entropy which has the property that once a constraint is removed the ...
1
vote
0answers
37 views

Intuition on Gibbs measures

I am (roughly) aware of the way Gibbs measures are used to solve physical systems (e.g. the Ising model). We can basically boil it down to pinpointing a Hamiltonian. My question is, consider a ...
1
vote
0answers
90 views

How to derive equation for time it takes photons to diffuse through the Sun

I am wanting to use the Rosseland radiative heat flux equation to find the time it takes for photons to diffuse through the sun. The answer I am wanting to derive is: $$\tau_D~\frac{\rho \bar C_p ...
0
votes
0answers
16 views

Application of the Mean Field Approximation for molecules

When I studied the Ising Model in a course on Statistical Physics one approach that was presented was to use the Mean Field Approximation. In the ocasion I've noticed that it is also called "molecular ...
3
votes
1answer
129 views

Why don't we observe spontaneous symmetry restoration in nature?

Why do we always observe spontaneous symmetry breaking in nature and not restoration? Does there exist some argument with the 2nd law of thermodynamics and the entropy of the universe increasing? If ...
2
votes
0answers
35 views

Decimation of a triangular lattice [closed]

Consider the network of spins shown below. The Hamiltonian is given by $$H = - \sum_{\langle i j k \rangle} [J \sigma_i \sigma_j \sigma_k + J_0]$$ with $J,J_o \geq 0$ and $\langle i j k \rangle$ ...