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

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How do you prove $S=-\sum p\ln p$?

How does one prove the formula for entropy $S=-\sum p\ln p$? Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law ...
6
votes
2answers
645 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 ...
16
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2answers
1k views

Is this Landau's other critical phenomena mistake?

There was an old argument by Landau that while the liquid gas transition can have a critical point, the solid-liquid transition cannot. This argument says that the solid breaks translational symmetry, ...
2
votes
1answer
369 views

Cross-field diffusion from Smoluchowski approximation

I'm reading An Introduction to Stochastic Processes in Physics by Don S Lemons. Problem 10.2 leads to a pair of equations: $dV_x = -\gamma V_xdt+V_y\Omega dt-V_y\sqrt{2\gamma dt}N_t(0,1)$ $dV_y = ...
0
votes
1answer
518 views

Lee-Yang circle theorem

what is Lee-Yang circle theorem and what is it used for ?? , i mean given a measure how can you know that is Ferromagnetic and hence all its zeros lie on a Circle ?? the Lee-Yang circle theorem proof ...
1
vote
1answer
151 views

Heuristic argument for the temeprature dependence of specific heat in the “low” temperature regimes

Here by "low temperature" I meant it in the scale of the characteristic $\hbar \omega$ of the system. One can calculate and show that in the low temperature regime $C_V$ of phonons goes like $T^3$ ...
2
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2answers
320 views

Identifying a critical phenomena?

I have a system with a number of measurables (in time). Some measurables are discrete some are continuous (within the measurement accuracy). How can I determine whether my system experiences ...
5
votes
2answers
337 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 ...
1
vote
1answer
279 views

Can somebody provide some sort of crash course on random walk and its problems at the level of a beginning undergraduate student in physics? [closed]

I really need some very simple discussions of random walk (probability). Couldn't get anything from class, more so from Reif. Thanks!
3
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1answer
156 views

Repulsive classical identical particles on a square lattice

I am not sure whether it is some well-known named model in statistical physics. I could not find it in any standard text-book that I know of. Let there be $N$ identical classical particles ...
7
votes
1answer
319 views

Force curve associated with squeezing a worm-like chain (WLC) between two parallel plates

Let's say I have a polymer, of contour length $L_p$ and persistence length $P$, positioned between two parallel plates separated by a distance $z$. I slowly squeeze the plates together until only ...
3
votes
1answer
242 views

Is this geometrical 'derivation' of Brownian motion legitimate?

Here's a simple 'derivation' of the Brownian motion law that after N steps of unit distance 1, the total distance from the origin will be sqrt(N) on average. It's certainly not rigorous, but I'm ...
7
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4answers
392 views

Applying the Maxwell–Boltzmann statistics to astrophysical objects

Quoting Wikipedia: In statistical mechanics, Maxwell–Boltzmann statistics describes the statistical distribution of material particles over various energy states in thermal equilibrium, when the ...
11
votes
2answers
504 views

Number density of LO and LA phonons as a function of temperature?

I'd like to know the how the number density of longitudinal optical (LO) and longitudinal acoustic (LA) phonons varies as a function of temperature of the material. Is there a simple expression for ...
15
votes
3answers
3k views

Is there any proof for the 2nd law of thermodynamics?

Are there any analytical proofs for the 2nd law of thermodynamics? Or is it based entirely on empirical evidence?
1
vote
1answer
514 views

Statistical physics of molecular dissociation of a diatomic gas

Say there are $N$ atoms of type $A$ in a box of volume $V$ and they are undergoing a reversible association-dissociation reaction $A + A = A_2$. Let an $A$ atom have mass $m$, and hence the molecule ...
3
votes
3answers
366 views

Is there any physics behind flocking?

There are many articles published in physics journals about flocking. Is there a physical reason for these phenomena or is it just because physics methods are being used to study collective motion? ...
9
votes
3answers
374 views

Can the entropy density of a spacelike singularity arbitrarily exceed the inverse Planck volume?

For the purpose of this question, let's restrict ourselves to BKL singularities. BKL cosmologies are homogeneous Bianchi type XIII and IV cosmologies which exhibit oscillatory chaotic behavior, ...
2
votes
1answer
806 views

Calculating the derivative of the average number of particles by the chemical potential

This should be a trivial calculation but somehow I have managed to get myself confused about this. The grand partition function is: $\mathcal Z = \sum_{N=1}^\infty \sum_{r(N)} {\text e}^{-\beta E_r ...
3
votes
1answer
273 views

Are black hole states completely mixed?

A completely mixed state is a statistical mixture with no interference terms, and (QMD, McMahon, pg 229): $$\rho = \dfrac{1}{n}I$$ $$Tr(\rho^2) = \dfrac{1}{n}$$ Are black hole quantum states ...
4
votes
1answer
439 views

Proving that the free energy is extensive

If I have two system of an Ideal gas $A$ and $B$ each of these system has a partition function: $Z_{A,B} = \left ( \frac{V_{A,B}}{\lambda_T} \right )^{N_{A,B}}$ Where: $\lambda_T = \left ( ...
7
votes
3answers
1k views

Once a quantum partition function is in path integral form, does it contain any operators?

Once a quantum partition function is in path integral form, does it contain any operators? I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where H is an operator, the Hamiltonian of the ...
3
votes
0answers
653 views

How do I derive the critical temperature for bose condensation in two dimensions?

In class we derived the 3D case, but there's a step I don't understand: $$ N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = ...
1
vote
4answers
365 views

'A' butterfly effect

If a butterfly did not flap its wings some time ago, but instead decided to slide for that millisecond, can this cause a tornado on the other side of the earth if we just wait long enough? Does this ...
0
votes
1answer
601 views

Derivation of relativistic energy

The concept of relativistic energy comes from it's conservation in relativistic mechanics for an elastic collision. It seems to me that another possible derivation could equate the energy of a single ...
6
votes
3answers
2k views

Collision time of Brownian particles

Let's assume two spherical particles $p_1$ and $p_2$ of finite radius $r_1$ and $r_2$, which are at locations $(\pm\frac{d}{2},0,0)$ a distance $d$ apart at initial time $t$. These particles diffuse ...
3
votes
1answer
1k views

Chemical potential interpretation

Something that has bothered me for a while regards the interpretation of chemical potential for different statistics. While I understand its meaning in metals (and its relation with the Fermi ...
4
votes
2answers
278 views

What does this observation of instantaneous velocity in Brownian particles mean?

I read this artice: Physicists Prove Einstein Wrong with Observation of Instantaneous Velocity in Brownian Particles “We’ve now observed the instantaneous velocity of a Brownian particle,” says ...
6
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4answers
3k views

Chemical potential

This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...
5
votes
0answers
151 views

Applicability of Baxter's method for IRF models

In a interaction-round-a-face model of $n^2$ particles in a lattice, a weight $W(a,b,c,d)$ is assigned to each face in the lattice based on the spins $a,b,c,d$ (listed say from the bottom-left corner ...
6
votes
2answers
953 views

Efficiency of Metropolis algorithm

Context is 1D Ising model. Metropolis algorithm is used for simulate that model. Among all possible spins configurations (states) that algorithm generates only states with the desired Boltzmann ...
9
votes
6answers
823 views

A die versus a quantum experiment

Let suppose you roll a die, and it falls into a hidden place, for example under furniture. Then although the experiment has already been made (the die already has a number to show), that value can not ...
14
votes
3answers
2k views

How Non-abelian anyons arise in solid-state systems?

Recently it has been studied non-abelian anyons in some solid-state systems. These states are being studied for the creation and manipulation of qubits in quantum computing. But, how these ...
12
votes
3answers
1k views

trying to understand Bose-Einstein Condensate (BEC)

I am a computer scientist interested in network theory. I have come across the Bose-Einstein Condensate (BEC) because of its connections to complex networks. What I know about condensation is the ...
4
votes
1answer
376 views

Is there a fully quantum-field theoretic treatise of Planck's Law for black-body radiation?

I recall from my undergraduate statistical mechanics and QM classes that Planck's Law may be derived fairly straight-forwardly by considering the density of states of EM radiation in thermal ...
3
votes
2answers
769 views

What happens in string theory beyond the Hagedorn temperature?

What happens in string theory when the temperature exceeds the Hagedorn temperature? Is that even possible? If yes, what is the nature of the phase transition and the phase beyond that? What happens ...
6
votes
4answers
817 views

Please clarify how entropy increases when matter gravitationally coalesces

On John Baez's website, http://math.ucr.edu/home/baez/entropy.html, he discusses the problem of how entropy increases when a cloud of ideal gas collapses gravitationally (no black holes - keeping it ...
12
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5answers
2k views

Can a single classical particle have any entropy?

recently I have had some exchanges with @Marek regarding entropy of a single classical particle. I always believed that to define entropy one must have some distribution. In Quantum theory, a single ...
8
votes
2answers
397 views

Shaking a jar of balls

A jar is filled with two types of balls, red and green. Red balls have radius $r_1$ and mass $m_1$, green balls have radius $r_2$ and mass $m_2$. If initially the balls are randomly placed throughout ...
7
votes
3answers
2k views

Partition function of a hydrogen gas

Hi I have a doubt (I'm not very expert in statistical mechanics, so sorry for this question). We consider a gas of hydrogen atoms with no interactions between them. The partition function is: $$ ...
0
votes
1answer
361 views

Given temperature, composition, column density, and radial velocity, can I find the bulk flow of a gas cloud?

We've got a hot star in the middle of a gas cloud. We point a spectrometer at the star, calculating the following attributes of our line of sight at the star through the cloud: Total number of ...
9
votes
1answer
1k views

Largest theoretically possible specific heat capacity?

What substance will have the largest specific heat capacity integrated from T=0 to, say, room temperature? In other words, given a finite amount of mass, what object or collection of objects has the ...
4
votes
1answer
821 views

For which systems is the equipartition theorem valid?

Under what conditions does a system with many degrees of freedom satisfy the equipartition theorem?
3
votes
5answers
561 views

Temperature of a System of molecules

Suppose I have a closed system with N molecules in it which are vibrating and all motion equations (rotation, translation and vibration) of the system are known along with any EM field equations in ...
2
votes
1answer
85 views

Why is $\rho_m$ proportional to the deviation from critical temperature in critical phenomena?

In Peskin and Schroeder's chapter 12 about the renormalization group, it is stated that the parameter $\rho_m=m^2/M^2$, where $m$ is the mass and $M$ is the renormalization scale, is proportional to ...
7
votes
3answers
371 views

Estimating Partition functions

I have a finite state ensemble with an energy functional (you can think of it as an ferromagnetic Ising model if you like), and I need very careful estimates of the partition function. What methods ...
3
votes
1answer
282 views

Entropy of a polymer contained in a sphere with infinitely thin chords

Imagine that I have a polymer (approximated as a freely diffusing, freely jointed chain with some number of subunits 'N'), and I place this polymer into a sphere of some volume 'V'. Next, I proceed to ...
4
votes
4answers
607 views

Where can I find a good classification for phase transitions?

I'm having a hard time to find a good (and modern) classification scheme for phase transitions and related universality classes. Can someone recommend a paper/book/site? Detailed mathematical aspects ...
3
votes
4answers
881 views

Accuracy of the Boltzmann equation

I have had this question for some time now. Hopefully someone can answer it. I know that the Boltzmann equation is widely regarded as a cornerstone of statistical mechanics and many applications have ...
5
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3answers
718 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 ...