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
6 views

Why is it inappropriate to calculate free energy change from end points alone?

In molecular dynamics, free energy changes are estimated using a variety of protocols to establish a path between the starting and ending states. The classic example is umbrella sampling in which a ...
1
vote
0answers
19 views

Brownian Ratchet Plausibility

Alright I'm going to throw whatever reputation I have on the line here. And yes this is a serious question. Apologies for the shoddy imagery. I had a couple ideas to get the Brownian Ratchet to ...
4
votes
0answers
37 views

How can I intuitively understand the particular form of the Boltzmann factor?

It is known that for a system at thermal equilibrium described by the canonical ensemble, the probability of being in a state of energy $E$ at temperature $T$ is given by the Boltzmann distribution: ...
0
votes
0answers
5 views

How does sphere packing fraction in a long cylinder change with sphere size? [migrated]

Earlier I had to cut up some materials into little pieces and fit them in a glass tube, and I wondered if it's better to cut the pieces as small as possible, or if it wouldn't matter. If we think ...
0
votes
1answer
61 views

Could the uncertainty principle theoretically be violated at 0 K? [duplicate]

Ok so please excuse me if the following mental argument is completely ridiculous or obviously flawed :P I was reading about how, even at 0 K (assuming we could experimentally reach such a ...
0
votes
0answers
18 views

Phase separation - density functional theory

I would like to get the equilibrium density profile $\rho(x)$ of a non ideal gas that has phase separated. I start by defining a simple free energy density. The total free energy $F[\rho]$ is a ...
1
vote
1answer
22 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 ...
33
votes
6answers
4k views

Is there a thermodynamic limit on how efficiently you can solve a Rubik's cube?

Suppose I build a machine which will be given Rubik's cubes that have been scrambled to one of the $\sim 2^{65}$ possible positions of the cube, chosen uniformly at random. Is it possible for the ...
2
votes
1answer
66 views

Quantum ideal gas - Canonical ensemble - Occupation number summation notation (Huang)

(Question at the end, in bold, marked with an b)) For the quantum ideal gas, the hamiltonian (operator) of the system is: \begin{align} \mathcal H=\sum_{i=1}^N H_i=\sum_{i=1}^N \frac{P_i^2}{2m} ...
0
votes
0answers
31 views

Partition function for a two state system

We have a system of two energy states and we treat classical distinguishable and indistinguishable particles respectively. For the distinguishable case I thought that all in the left one one left ...
1
vote
1answer
16 views

Reversible and Quasi static processes

Do we have any proof that reversible processes are always quasi static or is it just a fact that hasn't been violated till date? If there is a proof then please provide a link.
0
votes
1answer
21 views

Error in calculation of ideal fermi/bose gas [closed]

NOTICE: I am NOT only asking about a wrong sign, not a completely false result, so you might skip these kind of calculations! I was doing a calculation to get the first order approximation to the ...
0
votes
1answer
39 views

Sum over momentum states

In our lecture we used quite a couple of times that the sum over momentum states can be approximated by an integral over them. But instead of substituting $\sum_p \rightarrow \int d^3p$, we replaced ...
0
votes
0answers
17 views

Dimension of the Hilbert space of the restricted surface-on surface (RSOS) model

Right now I'm reading a paper on inversion identities for RSOS models, which you can find here. To give you a short introduction: The RSOS model is a face model, with a height variable assigned to ...
1
vote
1answer
22 views

Joule Thomson effect

I have difficulties to understand the Joule Thomson coefficient given on the wikipedia page. It says that $(\partial_p T) = \frac{V}{C_p}( T \alpha -1)$. Now my problem is that I don't know about ...
1
vote
1answer
37 views

Density depletion for Fermions

In my recent advanced statistical physics class, I read about the density depletion of Fermions, which are "defending" a given volume around them against other Fermions, while the exchange hole ...
4
votes
0answers
33 views

What is the argument for detailed balance in chemistry?

Detailed balance is an important property of many classes of physical systems. It can be written as $$ \frac{p_{i \to j}}{p_{j \to i}} = e^{\frac{\Delta G}{k_B T}},\tag{1} $$ where $i$ and $j$ ...
5
votes
0answers
83 views
+50

Definition of stress at the microscale

Take, for simplicity, a Lennard-Jones fluid below the critical temperature, which is to say that there is a phase separation into fluid and gas and thus an interface is formed. The macroscale picture ...
2
votes
0answers
32 views

Why is the isothermal compressibility of the ideal boson gas larger than of the classical ideal gas?

Recently I came across (or well, derived in a lecture) the isothermal compressibility for an ideal boson gas. This was done in the context of statistical physics, using the quantum version of the ...
1
vote
2answers
80 views

Velocity Maxwell-Boltzmann distribution for dummies

I have a volume with N molecules; I need to assign to each particle a velocity vector: $$|\mathbf{v}_{i}|=[v_{x}, v_{y}, v_{z}]^{T}$$ for the i-th molecule; the velocities must fallow the ...
1
vote
1answer
28 views

Can a Fermi gas and a Bose gas be both at the same pressure and temperature?

The title says it all: can a Fermi gas and a Bose gas be both at the same pressure and temperature? It comes from a quiz about statistical mechanics
2
votes
1answer
58 views

Correlation length in d>1 Ising model, at zero temperature

I am studying the renormalization group approach to the Ising model using as a reference Cardy's book "Scaling and renormalization in statistical mechanics". I cannot understand what happens in the ...
1
vote
1answer
51 views

Meaning of chemical equilibrium between two phases

Suppose two phases 1 and 2 of water, say ice and water, are kept in a closed container, at a fixed temperature $T$ and fixed pressure $P$? Then I have the following question: Is phase 1 in ...
3
votes
1answer
48 views

Difference between collisional and collisionless Boltzmann equations?

Reading an excellent answer, I've read about there are different Boltzmann statistics for a collision-less system (f.e. stars in a galaxy) and in a system with collisions (f.e. gas in a closed box). ...
2
votes
1answer
27 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} \, ...
2
votes
1answer
76 views

Geometry, Group Theory, and Statistical Mechanics

During the course of my first statistical mechanics course we generally concerned ourselves with a bulk amount of our system and considered it in terms of a set of lattice sites that had a state. How ...
0
votes
1answer
44 views

entropy of van-der-Waals gas [closed]

Consider a van-der-Waals gas of $N$ molecules with the equation of state $$P=\frac{NT}{V-bN}-\frac{aN^2}{V^2}$$ with constants $a,b>0$. To gather thermodynamical information about the system ...
1
vote
1answer
107 views

Why is the canonical partition function an exponential?

It makes intuitive sense that micro-states of higher energy occur with a lower probability and the exponential function has reasonable properties. However can a physical explanation be given to why ...
0
votes
1answer
43 views

assumption of molecular chaos and the Loschmidt paradox

The assumption of molecular chaos says the velocities of two colliding particles are uncorrelated and also independent of time. Boltzmann actually used this assumption in his formulation of the ...
1
vote
1answer
51 views

What is the cause for mechanical equilibrium in statistical mechanics?

In classical thermodynamics, mechanical equilibrium is defined as the state of a system in which there is no net flow of volume as there should be no net pressure within the system. Ok. ...
2
votes
1answer
57 views

What's the closed-form of the sum relating to the DOS of simple harmonic motion?

In order to calculate the density of states of single particle in the simple harmonic potential, we would calculate that $$ D(\epsilon)=\sum_{n}\delta(\epsilon-\epsilon_n) $$ where ...
0
votes
1answer
36 views

Fermions and Bosons

For fermions $$P-\frac{Nk_BT}{V}\geq 0 $$ and for bosons, $$P-\frac{Nk_BT}{V}\leq 0$$ What can we understand from these results.
0
votes
1answer
55 views

Summation to Integration in Statistical Mechanics

In Statistical Mechanics, what is the procedure of replacing this summation by the integration given by $$\sum_{\vec k} \rightarrow \frac{V}{(2\pi)^3} \int_{0}^{\infty} 4\pi k^2 dk$$
0
votes
1answer
48 views

Average Occupation Number in Bose Einstein Statistics using Grand Canonical Ensemble

If $Z=Z(z,V,T)$ is the Grand canonical Partition function, $\beta =\frac{1}{k_BT}$,$z=e^{\beta \mu }$ is the fugacity and $\epsilon_{\vec p}$ is the energy of a single particle in pth momentum state, ...
0
votes
0answers
36 views

Statistical Mechanics of interacting Particles. Quantized Fields. Solving Integral? [migrated]

Hi everyone How we can analytically without using a software solve below integral . Chapter 11 of Pathria (edition 1). and x is dimensionless.
0
votes
0answers
10 views

Statistical Mechanics of Interacting particles [duplicate]

I am looking for other references about Statistical Mechanics of Interacting particles about Just the Method of Quantized Fields.This is the Title of Chapter 11 of Pathria (edition 1). If someone know ...
1
vote
2answers
97 views

What is the difference between classical thermodynamics and statistical mechanics? [duplicate]

What is the difference between classical thermodynamics and statistical mechanics? To me, they are greatly different but are different approaches for explaining same thing. But I do prefer ...
1
vote
1answer
28 views

Derivation of Fermi level for T>0

I am working through the derivation of the Fermi level $ \mu_0$ for T>0. However, at one point in the notes I have, it states without any explanation that: $$ \int_0^\infty F'(\epsilon) ...
1
vote
1answer
31 views

Pressure in the grand canonical ensemble when momentum integration limits depends upon volume

When one does not want to consider the thermodynamic limit, it is possible in some systems to consider a dependance of the volume on the integration limits of the momentum. For example: $$\mathcal{Z} ...
0
votes
2answers
61 views

What is the solution for the apparent contradiction of Second law due to energy fluctuation?

A system has maximum entropy when it has reached thermal equilibrium. But as statistical mechanics say, there is always an otherwise infinitesimal probability of particles to confine at a corner of ...
1
vote
2answers
42 views

Magnons contribution to spontaneous magnetization

In Statistical Physics part II of Landau's course in theoretical physics it is stated that the magnon part of the spontaneous magnetization can be calculated as $$ M_m \equiv M(T) - M(0) = ...
0
votes
1answer
30 views

Meaning of reversibility and quasistatic processes

A process in a closed system is reversible if the entropy change is $dS = \frac{dQ}{T}$. A process is quasistatic if a process is infinitely slowly. Now, if a process is reversible, this means ...
0
votes
1answer
22 views

Relation between isentropic/isenthalpic to adiabatic?

We have $dQ = T dS$. Does this imply that a process is adiabatic $dQ = 0$ if and only if it is isentropic $dS = 0$ for any process? This does not sound right, as this would mean that there is no ...
1
vote
1answer
31 views

Ideal chain / entropic spring - what is the *microscopic* force?

The ideal chain is the classic example of an entropic force. Usually one derives this force from the fundamental relation describing forces in the canonical ensemble: $$ \tag 1 F = (\partial \langle E ...
0
votes
2answers
56 views

Thermal Equilibrium and Canonical Ensemble

1 - Are two closed systems (with fixed volumes and of the same gas) in thermal equilibrium equivalent to two isolated systems at the same temperature? 2 - In the canonical ensemble, the "small ...
1
vote
0answers
42 views

Good Resource for Classifying Statistical Mechanics Problems [closed]

I've grown very interested in statistical mechanics ever since I took my first course in it. However, it feels like it is just overflowing with many types of problems and plenty of categories to ...
3
votes
0answers
73 views

Does Noether's theorem apply to entropy?

Entropy appears to have a translation symmetry - adding some constant value to it doesn't appear to my fairly rudimentary understanding of physics alter the actual physics. Is this correct? Now ...
1
vote
1answer
43 views

Definition of Entropy for reversible and irreversible process

$\int \dfrac{\delta Q}{T}$ can't be used to calculate entropy of an irreversible process. If you happen to know heat supplied and temperature at which it is supplied for just an instant. Can you then ...
0
votes
0answers
24 views

What is the central charge of the disordered $q$-state Potts model, for large $q$?

The central charge of a model, is, heuristically related to the number of microscopic degrees of freedom. Is there a simple argument for the asymptotic behavior of the central charge for the ...
0
votes
1answer
41 views

Efficiency larger than one?

The efficiency of a heat engine is the work we can do divided by the heat we take out of the hot reservoir. This quantity is always $ \le 1$. The efficiency of a heat pump is the heat we can release ...