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

learn more… | top users | synonyms

0
votes
0answers
11 views

Questions on the degenerate ground states and Lieb-Schultz-Mattis theorem?

For example, let's consider a $N$ spin-1/2 system on a lattice described by the Hamiltonian $H$. My questions are ordered as follows: (1) If $H$ has either global $SU(2)$ spin-rotation symmetry or ...
8
votes
1answer
72 views

What precisely does the 2nd law of thermo state, considering that entropy depends on how we define macrostate?

Boltzmann's definition of entropy is $\sigma = \log \Omega$, where $\Omega$ is the number of microstates consistent with a given macrostate. If I understand correctly, this means that it only makes ...
3
votes
1answer
41 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
3
votes
2answers
150 views

Connection between QFT and statistical physics of phase transitions

I have heard that there is a deep connection between QFT (emphasized by its path-integral formulation) and statistical physics of critical systems and phase transitions. I have only a basic course in ...
3
votes
1answer
76 views

Is there a known equation for evolution of classical particle probability density?

Suppose we have some very imprecise knowledge of classical particle's coordinates and momentum: what we can only tell is the probability density to find it in some point of phase space. This is ...
3
votes
0answers
94 views

Quantum entaglement and the arrow of time

I have seen several claims to that quantum mechanics is required to explain the arrow of time which I take to mean the macroscopic irreversibility of physical systems. This is presumably to resolve ...
1
vote
1answer
183 views

Calculating the change in entropy in a melting process

I have a homework question that I'm completely stumped on and need help solving it. I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
0
votes
1answer
80 views

2nd order phase transition trouble deriving coefficient in fluctuations analysis

I can't get one of the coefficients in the equation for $T < T_c$ in the bottom, specifically the equation with the factor of two. any help appreciated. Consider an ising type expansion of the ...
3
votes
0answers
33 views
+50

What real experimental systems are well-described by Glauber-Ising spins?

I'm hoping for references to actual physical systems in which all or at least most of the following can be simultaneously characterized: the spin flip rate, the temperature, and a relaxation or ...
2
votes
2answers
51 views

Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
1
vote
0answers
40 views

Ising model. What is large fluctuations of magnetization?

My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical ...
2
votes
1answer
82 views

Quantum Fourier Transform and Entropy

QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of ...
1
vote
0answers
37 views

Chemical potential of photons

Why do photons have zero chemical potential and what is its the physical significance? From what I know the chemical potential could be interpreted as the energy per unit particle that is put into a ...
1
vote
0answers
55 views

Volume of phase space

Consider the microcanonical description of an extreme relativistic ideal gas of $N$ particles in three dimensions, characterized by the energy-momentum dispersion $E = pc$. Compute the volume of the ...
1
vote
2answers
59 views

Free electron gas in two dimensions

Can someone give a qualitative description on why the density of states for a two dimensional free electron gas is independent of energy while it is not in one and three dimensions? In one dimension ...
0
votes
1answer
16 views

Probability distribution of two particle types system

Suppose that particles of two different species, A and B, can be chosen with probability $p_A$ and $p_B$, respectively. What would be the probability (and distribution) $p(N_A;N)$ that $N_A$ out of ...
2
votes
1answer
67 views

Statistical count

I am reading the book"Heat and Thermodynamics" by Mark Waldo Zemansky and Richard Dittman. In the chapter "Statistical Mechanics" it says if I have $N_{i}$ distinguishable particles in any of $g_{i}$ ...
1
vote
1answer
447 views

Occupied lattice sites, determining number of microstates and energy

A solid consisting of $N$ molecules on a lattice of $N$ sites is isolated from its environment, and has energy $E$. Each molecule is fixed in position and independent of all others. It can be in any ...
0
votes
2answers
98 views

What are correlated magnetic moments?

My book has the following sentence and I don't understand what correlation or lack of correlation means: At high temperature the magnetic moments of adjacent atoms are uncorrelated (to maximize ...
0
votes
1answer
58 views

Failure of a simple stat mech simulation

so I did a simple simulation that I thought would yield a Boltzmann distribution, but it failed to, and I was wondering if anyone has insight into why it failed. Ok, so I had a simple discrete system ...
0
votes
0answers
37 views

Is it possible to define a notion of temperature in a microcanonical ensemble?

I am thinking of a mircrocanonical ensemble as a finite system for which the number of particles, volume and the total energy is fixed. Is there a more refined view of this? Can I think of ...
2
votes
1answer
69 views

RMS Free Path vs Mean Free Path

I am trying to determine the mathematical difference between mean free path and root-mean-square free path. For an ideal gas, the relaxation time is $$\tau=\frac{1}{\sqrt2 \pi nd^2 \bar v}$$ and the ...
4
votes
1answer
74 views

A real gas with gravitation-like interaction

Consider a system (a gas) of point-like particles with a gravitation-like interaction (potential) $V(r) \sim \frac{1}{r}$ between pairs of them. One can rule out statistically that two particles will ...
2
votes
0answers
53 views

Statistical mechanics of a coin toss

I'd like to ask some questions about flipping two coins related to statistical mechanics, e.g. microcanonical distribution, phase space distribution function etc... after I rephrase the coin flipping ...
2
votes
1answer
83 views

Can I express the heat flow of a fluid in terms of estabilshed characteristics of the velocity distribution?

If $\rho$ is the mass density of a fluid and $A({\bf v})$ is an function of the velocity, which is distributed according to $f({\bf v})$, we have an averaging process $A\mapsto \langle A\rangle:=\int ...
1
vote
3answers
175 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
72 views

Thermodynamics, chaperones : How to model polymer fragmentation

Living polymers are well described by equilibrium statistical physics. Now I would like to consider a case were living polymers undergo fragmentation due to chaperones. I can think of a kinetic ...
1
vote
2answers
110 views

Entropy Maximization using undetermined multipliers

This is from Problems in Thermodynamics and Statistical Physics by P.T. Landsberg A system can be in any one of N states. Using the method of undetermined multipliers to show for the maximum ...
28
votes
4answers
705 views

How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
1
vote
0answers
26 views

phase-space volumes or cells for N particle system

For N non interacting spinless particles in a volume, we have 3N degrees of freedom and we can divide the phase space into 6N dimensional cells of volume h raised to power 3N. And each cell ...
0
votes
1answer
124 views

Virial Theorem and the Energy in a Gas

I clearly am interpreting the Virial Theorem incorrectly, but I don't know how. In dipole gases, the molecules can exhibit five kinetic modes, while they can only experience 2 potential modes. Doesn't ...
1
vote
1answer
113 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
2
votes
0answers
32 views

Three-body correlation function in kinetic theory

In Kinetic Theory, one studies the evolution of a system of $N$ particles interacting with each other. We use the notation $\boldsymbol{w}_{i}$ to describe the coordinates in phase-space of each ...
0
votes
1answer
93 views

General way to model baths? Harmonic Oscillators valid?

I am trying to model an open system interaction without making strong assumptions on coupling strength or temperature. In general i understand that open systems are modeled by a Lindbladian, but as ...
3
votes
2answers
75 views

Statistical Mechanics - Distribution of Energies

Consider a state space $\mathbb{X}$. The probability density function under a canonical ensemble is given by the Boltzmann distribution $$\pi_{\mathbb{X}}(x)=\frac{e^{-\beta ...
0
votes
2answers
37 views

Is there an analogue to the role of vapor in liquids and gases, but for solids and liquids?

It seems common for an ordered phase to have some amount of disorder present. For example, the average moment of a ferromagnet is less than maximum except at T=0 due to the presence of fluctuations. ...
4
votes
0answers
73 views

Nonequilibrium thermodynamics in a Boltzmann picture

The Boltzman approach to statistical mechanics explains the fact that systems equilibriate by the idea that the equillibrium macrostate is associated with an overwhelming number of microstates, so ...
0
votes
2answers
81 views

Non-Equilibrium Statistical Mechanics

Can anybody please explain what is the difference between equilibrium state and steady state, as quoted by book by Degroot and Mazur. Also, does violation of Principle of Detailed Balance means the ...
-2
votes
0answers
20 views

Suggestions about these books [duplicate]

Which are the best books for the following( introductory level)? quantum mechanics classical mechanics statistical physics particle physics
3
votes
3answers
288 views

Leap from photon gas energy distribution to black body radiation?

I remember considering in class in college, the case of a photon gas trapped in a d-dimensional box as a subject of interest, whose energy distribution, heat capacity, etc. should be calculated. ...
2
votes
1answer
62 views

Lennard-Jones induced pseudo-molecules

It can be shown that the Lennard-Jones potential - which describes the interaction between particles in non-ideal gases - gives rise to pseudo-molecules: after a triple "collision" of three ...
3
votes
4answers
3k views

What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
1
vote
0answers
34 views

Boltzmann distribution: derivation from canonical distribution

I'm trying to understand the Maxwell-Boltzman Distribution, and in particular the derivation from the boltzman distribution for energy. I have successfully created an incorrect derivation, but I'm not ...
8
votes
5answers
100 views

How can point-like particles in an ideal gas reach thermodynamical equilibrium?

Having learned that the particles of an ideal gas must be point-like (for the gas to be ideal) I wonder how they can reach thermodynamical equilibrium (by "partially" exchanging momentum and energy). ...
1
vote
3answers
334 views

Mathematical proof of non-negative change of entropy $\Delta S\geq0$

I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that $$\Delta S\geq0$$ via Clausius' theorem. My question is, how can I prove this in a ...
11
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
25 views

Can electrons coincidentally flow along a circuit to cause current?

My understanding of circuits which are not supplied an e.m.f. is that the electrons randomly just flow about in random directions, and since there's so many of them, probability dictates that any ...
8
votes
3answers
595 views

Why must the particles of an ideal gas be point-like?

Why is a gas of elastically colliding hard balls of finite size not ideal? Respectively: Why is it essential that the particles of an ideal gas are point-like? Especially: Which ...
4
votes
1answer
108 views

Which transformations are canonical?

Which transformations are canonical? Why do canonical transformations preserve the measure of integration in phase space?
4
votes
1answer
300 views

Renormalization Group and Ising with d=1 and D=1

I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations $K'(K)$, $q(K')$ $K(K')$, $q(K)$ between the coupling costants. My problem arise ...