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

learn more… | top users | synonyms

1
vote
2answers
132 views

The statistical interpretation of Entropy

I recently got introduced to the Statistical Mechanics, particularly, the Statistical Interpretation of Entropy and am utterly confused regarding the following problem: Imagine a box with two ...
1
vote
1answer
105 views

Calculated heat capacity different (lower) from experimental value?

When treating gases as ideal, classical systems, the heat capacity can be found by multiplying the number of independent degrees of freedom by 1/2k, where k is Boltzmann's Constant. However, these ...
2
votes
3answers
196 views

What happens to the $PV=nRT$ formula as the gas enters the liquid phase?

The formula $PV = nRT$ explains the relationship between pressure, volume and temperature in terms of the quantity of gas present in a container. I'm trying to understand how these are related once ...
1
vote
0answers
27 views

Partition Function And Macroscopic Properties

In renormalization group transformations, partition function is fixed. My question is which thermodynamic properties are fixed in a renormalization group transformation.
1
vote
0answers
14 views

Canonical treatment of thermalization of two gases at different temperatures

I'd like to understand the thermalization process when two gases of different species and different temperatures are allowed to mix in an insulated container, interacting only through an elastic ...
2
votes
2answers
401 views

Understanding entropy [duplicate]

I am currently doing some research on entropy and I am trying to get my head around the concept. One thing that I am getting right now is that entropy is just an application of probability and ...
7
votes
1answer
276 views

What is the origin of blackbody radiation? [duplicate]

Of course I know what black-body radiation is, like everyone else who has taken a thermal or statistical physics course. But it was recently pointed out to me that one thing that is rarely taught ...
1
vote
1answer
62 views

Confused by Langevin Equation

Trying to understand the Langevin Equation. In particular, this passage from a Wikipedia article has me confused (section: "Thermal Noise in an Electrical Resistor"): $\frac{dU}{dt} ...
2
votes
0answers
38 views

dependence of braiding matrix element on the fusion product of anyons

In the case of Majorana fermions (MFs), one knows that if one braids MF $a$ with MF $b$, then braiding matrix element $R^{c}_{ab}$ depends on the state $c$ which is the fusion outcome of $a$ and $b$. ...
4
votes
1answer
102 views

Calculating the number of particles in phase space

I'm looking at the first part of question 7 here (I'm a mathematician trying to self teach some physics, this isn't a homework assignment so I'm just in need of hints)! I'm struggling to make sense of ...
2
votes
1answer
59 views

Is kinetic energy related to chemical potential?

I wonder if the kinetic energy written as $\frac{d\mathbf x}{dt}\cdot d\mathbf p$ is related to chemical potential? I ask because if I use $\mathbf p = m \frac{d\mathbf x}{dt}$ as a constitutive ...
0
votes
0answers
63 views

Probability density function of simple Mass-Spring system

We know that after long run of simple mass-spring system, there should be a probability of finding the mass at certain points between -A and A.. Obviously in probability of finding the particle near A ...
5
votes
2answers
301 views

Quantum and Classical Liouville operators

In the Heisenberg picture of Quantum Mechanics, for an observable $\hat{A}$, we have the famous Heisenberg equation giving the time evolution of the operator: ($\hat{H}$ is the Hamiltonian operator) ...
0
votes
2answers
181 views

Diffusion of gas into vaccum

I'm interested in solving the diffusion equation for gas in vacuum. I have a general question and a more specific questions. What I know: The Diffusion Equation: For density function ...
26
votes
6answers
3k views

How can fast moving particles gain energy from slow moving ones?

Imagine a large diameter piston filled with water connected to a small funnel. When you press on the piston slowly but with considerable force the water will move very quickly from the funnel in form ...
1
vote
1answer
34 views

BEC in interacting systems

What is your thought on the following statement: "any system of (weak/ strong) interacting bosons, in liquid phase, will form a condensate at T=0". Any example or counter-example ? Will dimensionality ...
3
votes
1answer
187 views

Calculation of long-range forces in Molecular Dynamics - Ewald summation

I am trying to write a code to calculate the potential and forces, for the same using ewald summation.For this purpose, the formula for potential and force I have used is : $$ U = U^{(r)} + U^{(k)} ...
1
vote
1answer
221 views

About thermodynamic beta

First of all, I'm not majoring this part and just finding some answer about Arrhenius rate equation: $$ v \propto \exp\left(-\frac{E_a}{kT}\right) .$$ To derive this relation, I started with ...
0
votes
1answer
75 views

Is Maxwell-Bolzmann a Normal (Gauss) distribution or a Chi distribution?

I was sure that the Maxwell-Bolzmann was a Normal distribution, but then I read that it was a Chi distribution on Wikipedia.
0
votes
2answers
48 views

Energy transfer in form of work or heat?

Suppose a system A which is a vessel of water with two electrodes, connected by a resistor, placed in the water. If you apply voltage to the electrodes, energy is transferred from the battery (not ...
0
votes
0answers
44 views

Speed of electrons at given temperature in non Hydrogen-like atoms

I may be somewhat confused on the topic, so please excuse me if this is really basic. For the Hydrogen atom, one can easily derive the expectation value of the electron's speed: $$ \langle v \rangle ...
0
votes
0answers
437 views

What is the physical meaning of a Partition Function in Statistical physics?

In many places in statistical physics we assume the partition function. To me the explanations after partition functions are most of the times clear but always wonder why a partition function and what ...
1
vote
3answers
141 views

Langevin Equation - Stochastic Differential Equation. What are the subtleties?

I am trying to find out the motion of a particle in 3D governed by the Langevin equation, numerically. Anyway, the Langevin equation is given by $$m \ddot{x} = -(6\pi a\nu) \dot{x} + F_b $$ where ...
0
votes
1answer
43 views

What is meant by the expression “Markovian dynamics”

I know what a Markov chain is but what does it mean in physics when I say that I assume Markovian dynamics? For example in Quantum Mechanics, I read that it means that the time evolution can be ...
-1
votes
1answer
278 views

Dr. Pierre-Marie Robitaille: On the Validity of Kirchhoff's Law

Lately I've been researching about the black-body spectrum and the historical development of Planck's Law. I mainly wanted to understand a little bit more why many different objects (Stars, Hot ...
0
votes
1answer
50 views

Temperature increase during friction

There is pin made of Asbestos and two disc material Aluminum and steel in first experiment i used Aluminum disc with asbestos pin in wear test the disc is rotating and the asbestos was in frictional ...
0
votes
1answer
40 views

The different in wear test when using Aluminum and Steel disc in pin on disc apparatus

In wear test of pin on disc apparatus i found that mass loss of pin when i used Aluminum disc is higher than when i used Steel disc under the same conditions ,pressure, velocity and contact time can ...
4
votes
1answer
98 views

Is the MaxEnt “interpretation” of statistical mechanics the current mainstream approach?

I've only recently started studying statistical mechanics and I'm quite confused with the MaxEnt and anti-MaxEnt ideas. I'm looking for a concise answer, if it is possible, not really a description ...
0
votes
0answers
55 views

Difficulty in understanding Maxwell Boltzmann distribution in case on ions in a field

I learned that the velocity of molecules obey Maxwell Boltzmann (MB) distribution at a Temperature T. If I have ions of mass 'M' accelerated to 2eV in a specific region. As the ions are not ...
1
vote
1answer
118 views

Expected value of an operator in the microcanonical ensemble

I am following professor David Tong's lecture notes on Statistical Mechanics and on page 9 of this file http://www.damtp.cam.ac.uk/user/tong/statphys/one.pdf he states that the expected value of an ...
1
vote
0answers
42 views

What is the relation between scattering amplitudes, fluctuations, response functions and correlations in macroscopic equilibrium systems?

In Kardar's book Statistical Physics of Fields, he mentions that that correlations at different length scales can be measured by scattering. If its electric correlations, you would scatter light and ...
2
votes
1answer
93 views

Is the $\mu VE$ ensemble possible to formulate?

I have recently learned about ensembles in statistical mechanics, and I've seen multiple applications and interpretations of the EVN (microcanonical), TVN (canonical), $\mu$VT (grand canonical) and ...
1
vote
2answers
139 views

Reference for mathematics of statistical mechanics

I'm looking for materials (books, articles, etc) which focus ONLY on the mathematics of statistical mechanics (as I have no background in physics). The materials may have some simple explanations or ...
0
votes
1answer
40 views

Is there a way to get the Bethe Roots, that belong to a given eigenvalue of the transfer matrix?

(Quantum) integrable systems, that belong to solutions to the Yang-Baxter-equation, are often solved by the (algebraic) Bethe Ansatz. Solutions to the Bethe-equations lead to the eigenvalues of the ...
3
votes
2answers
290 views

Laplace transform of partition function a general result or a mathematical result?

In the following derivation I am trying to show that the function $Z_C(\beta)$ is obtained from the function $Z_M(E)$ by Laplace transform. Let, \begin{equation} \frac{1}{Z_M}\frac{\partial ...
0
votes
3answers
42 views

How to conserve energy with electrical noise?

If a resistor experiences thermal noise, it will dissipate energy to the environment. But where does the resistor's energy come from? It seems that it will just lose energy until ran out.
7
votes
4answers
401 views

How is Liouville's theorem compatible with the Second Law?

The second law says that entropy can only increase, and entropy is proportional to phase space volume. But Liouville's theorem says that phase space volume is constant. Taken naively, this seems to ...
3
votes
1answer
274 views

The Liouville equation and the BBGKY hierarchy.

The Liouville equation of motion is written in terms of an $N$ particle distribution $f_N$. \begin{equation} \frac{\partial f_N}{\partial t}=\{H,f_N\} \end{equation} Where $\{\cdot ,\cdot \}$ is the ...
3
votes
0answers
69 views

Classical Statistical thermodynamics phase space and residue $h$

In classical statistical mechanics we have to divide the partition function by a factor of $1/h^n$. In almost every calculation of a real quantity this cancels out and is thought to be a remnant of ...
1
vote
0answers
58 views

Is there a local canonical ensemble partition function for a Bose-Einstein gas?

The grand canonical partition function for a Bose-Einstein gas is $$ Z_{\text{grand bos}} = \exp \left( \sum_{j=0}^{\infty} -\ln \left( 1-e^{\beta(\mu-\epsilon_j)} \right)g_j \right) $$ where $\beta$ ...
0
votes
0answers
34 views

Books that cover Mode-Coupling Theory

I am looking for a book that covers the schematic mode-coupling theory and that are not too arcane (i.e., recent book). Basically the only book so far on this I have come across is "nonequilibrium ...
0
votes
1answer
58 views

Fermi energy on a “fermion pre-gas model”

I'm having serious trouble while trying to follow an example from Callen's "Thermodynamics and an introduction to Thermostatistics" regarding the definition of the Fermi energy. In said example one ...
0
votes
1answer
90 views

Why is the correlation of an observable and its derivative zero?

Why is the correlation of an observable and it's derivative zero? And why does this not only hold for $\langle A(t) \dot A(t) \rangle $ but also for $\langle A(0) \dot A(t) \rangle $ ? These averages ...
2
votes
2answers
232 views

Multiplicity vs Partition function

I'm a little confused between all the different notations for the multiplicity and partition function. They're not the same thing, are they? I know that entropy can be expressed as $ S = k \ln\Omega ...
0
votes
1answer
32 views

Adjoint Fokker-Plank operator

In Zwanzig's book "nonequilibrium statistical mechanics" he defines the Fokker-Plank equation for a probability distribution $f$ and with it an operator $D$: $${ \partial f(a,t) \over \partial t} = ...
3
votes
3answers
96 views

Does the ratio of thermal energy to planck's constant have physical significance?

I realized that I had never noticed that $\left[ \frac{\hbar}{k_B T} \right]=$ Time. At $T \approx 300 K$, we have $\frac{\hbar}{k_B T} \approx 10$ fs. What, if anything, does this quantity mean? Does ...
0
votes
1answer
181 views

What is the physical fundamentals of Pascal's law

Pascal's law or the principle of transmission of fluid-pressure (also Pascal's Principle) is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible ...
3
votes
1answer
166 views

Critical temperature and lattice size with the Wolff algorithm for 2d Ising model

When I run my implementation of the Wolff algorithm on the square Ising model at the theoretical critical temperature I get subcritical behaviour. The lattice primarily just oscillates between mostly ...
1
vote
1answer
57 views

What's the difference between the Fermi level and the electrochemical potential?

I was asked in a Thermostatistics test to compute the electrochemical potential $\mu(T)$ and the Fermi level $\epsilon_F$ for a system of non-interacting fermions, with two possible energetic states ...
0
votes
1answer
47 views

Why classical open system and Bose-Einstein condensate are not fundamentally the same?

The classical partition function for an open system is given as $$ Z_{\text{max}} = \sum_{N=0}^{\infty} \dfrac{h^{-N}}{N! } \prod_{j=1}^{N} \left( \sum_{i=0}^{\infty} e^{-\beta (E_{ij}-\mu)} g_{i} ...