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

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334 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 ...
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1answer
265 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
154 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
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1answer
316 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
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1answer
238 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
370 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 ...
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2answers
484 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 ...
14
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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?
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1answer
493 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 ...
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3answers
362 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
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3answers
370 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
742 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
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1answer
417 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
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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
639 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
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4answers
361 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
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1answer
583 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
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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
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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
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2answers
268 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
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0answers
148 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
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2answers
916 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
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6answers
807 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
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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 ...
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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
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1answer
370 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
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2answers
728 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
760 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 ...
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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
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2answers
394 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
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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: $$ ...
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1answer
358 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
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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
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1answer
782 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
546 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
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3answers
358 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
281 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
584 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 ...
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4answers
846 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
689 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 ...
10
votes
2answers
312 views

What is known about some massive Gaussian models on a lattice?

Recently I started to play with some massive Gaussian models on a lattice. Motivation being that I work on massless models and want to understand the massive case because it seems easier to handle ...
12
votes
5answers
4k views

Difference between thermodynamics and statistical mechanics

I've just finished a class a few weeks ago which taught thermo and stat mech, and I still don't know the exact difference between the two. Can someone help clear this up for me? (Yeah it's sad, and ...
4
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5answers
2k views

Is temperature in vacuum zero?

From Wikipedia entry on Kinetic Theory The temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms. Now if I remove all the particles from the box shown ...
9
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3answers
1k views

To calculate the correlation functions of an XX spin chain, Wick's theorem is used. But is it valid for a chain of any size?

The correlation functions found in Barouch and McCoy's paper (PRA 3, 2137 (1971)) for the XX spin chain use a method which uses Wick's theorem. For the zz correlation function, this gives $\langle ...
7
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3answers
984 views

Zero magnetization of spin model without external magnetic field

For a given Hamiltonian with spin interaction, say Ising model $$H=-J\sum_{i,j} s_i s_j$$ in which there are no external magnetic field. The Hamiltonian is invariant under transformation $s_i ...
10
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1answer
717 views

Which areas in physics overlap with those of social network theory for the analysis of the graphs?

I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in ...
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4answers
402 views

Irreversible expansion and time reversal symmetry

Suppose there are N non-interacting classical particles in a box, so their state can be described by the $\{\mathbf{x}_i(t), \mathbf{p}_i(t) \}$. If the particles are initially at the left of the box, ...