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

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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 ...
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1answer
73 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 ...
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0answers
32 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 ...
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1answer
80 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 ...
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2answers
128 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 ...
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0answers
29 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 ...
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2answers
222 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 ...
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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.
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4answers
296 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 ...
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1answer
150 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 ...
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58 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 ...
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51 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 $\beta$ ...
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29 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 ...
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34 views

about Conservation laws and Correlation function

I'm reading a review paper by Gorden Baym-(http://www.worldscientific.com/doi/abs/10.1142/9789812793812_0002) In the second part, he raised that: According to conservation law $\frac{\partial ...
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1answer
49 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 ...
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1answer
78 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 ...
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2answers
108 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 ...
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1answer
24 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} = ...
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3answers
92 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 ...
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0answers
45 views

Wick's theorem: Classical Version. Derivation question and what happens with odd moments? [closed]

I am trying to prove the classical version of Wick's theorem: For a set of random variables ${a_i}$, with covariance matrix $M$ and $\rho(\vec a)$ a Gaussian probabilitiy density: $$\langle a_j a_k ...
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1answer
110 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 ...
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1answer
117 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 ...
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1answer
46 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 ...
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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} ...
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34 views

What does the particle to volume density physically mean for Bose-Eisenstein condensate?

The average number of particles $\langle N\rangle$ for a Bose-Eisenstein condensate in 3D is given as $$ \dfrac{\langle N\rangle}{V} = \dfrac{V^{-1}}{e^{\beta (0-\mu)}-1} + \int_{0}^{\infty} ...
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1answer
63 views

Good book for learning fluid statistics

I'm currently using Gray and Gubbins Theory of Molecular Fluids to learn about the statistical physics of fluids. It may be a fine reference text, but I'm not impressed with it as an introduction to ...
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1answer
315 views

Simpler derivation of Sackur-Tetrode equation

Is there a reason the following derivation for the Sackur-Tetrode equation is not common? I am teaching a lower undergraduate level class and would like to derive it with simpler terms of only using ...
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2answers
109 views

What are the definitions of microstates and macrostates?

I have been looking up definitions for microstates and macrostates of a thermodynamic-system. I am looking for clear conditions for systems to be in the same macro- or microstate, but have had no ...
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1answer
65 views

Order parameter in Landau's theory for second order phase transition

Above is a screenshot of Kadanoff's review article "more is the same". The free energy in Landau's theory is very well known, but the highlighted sentence seems to be quite confusing. First of all, ...
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1answer
38 views

How photons get distributed in a system?

Let's say I'm in a room, and there are plenty of things in my room like carpet,mirrors,glass and other stuff.And I see there are shadow regions and fully bright regions, and I want to know how photons ...
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28 views

Relaxation time approximation in anisotropic potential scattering event

In relaxation time approximation (RTA) of Boltzmann transport theory, the relaxation time is calculated by $\frac{1}{\tau(\mathbf{k})}=\frac{2 \pi}{\hbar V}\sum_{\mathbf{k^{'}}} \delta ...
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1answer
165 views

Calculate pressure from partition function with separated volume geometric parameters?

How does one calculate the pressure from the partition function if it is specified in terms of three parameters defining the space of which the gas occupies, but all three parameters are not always ...
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94 views

Why does Landau theory not fail when dealing with a first order phase transition?

Here is a problem where I can do the calculation, but I am not understanding the philosophy behind it. It is about Landau theory: The Landau theory of phase transitions is based on the idea that the ...
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3answers
352 views

What is the physical meaning of the Lindblad operator?

I read the wikipedia article on the Lindblad operator, but I still don't understand what this operator is supposed to describe. I therefore considered setting up an example in order to get the idea. ...
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1answer
165 views

Is average kinetic energy equal to the total thermal energy of a gas?

"Average KE" as in this equation: $$K_{average} = \frac{3}{2} kT$$ Since potential energy in ideal gas model is eliminated, I guess this equation is also for the total thermal energy of a gas/a ...
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84 views

Exact expression for the coefficient in Bloch-Grüneisen (BG) formula?

In most representations of the BG formula, there is a coefficient (usually left vague as an experimental parameter, but sometimes written out "analytically") in front of the integral: $$\rho=\rho_0 +A ...
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1answer
95 views

Drag force acting on a disk in a 2D system

I have a 2-dimensional system with behavior governed by Langevin dynamics in which disks (circles) move through a fluid. In the Langevin equation, there is a velocity-dependent term that accounts for ...
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1answer
65 views

Why is Fermi-Dirac type of distribution used in semiconductors?

We assume that distribution of electrons follows Fermi-Dirac distribution / statistics in semiconductor model which will help to find the concentrations of electron and holes and the relationship ...
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0answers
38 views

Simple mean-field “lattice gas” model [closed]

I'm having some conceptual problems with a simple mean-field "lattice gas" model and I'd be glad if someone could help me go further. Basically the model consists of the following hamiltonian: $$ H ...
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0answers
41 views

A functional average calculation confusion within Gaussian planar model's RG

I am trying to follow some detailed calculation in a famous paper [John, B. Kogut, Rev. Mod. Phys. 51, 659 (1979), An introduction to lattice gauge theory and spin systems]. More precisely, please ...
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0answers
40 views

bose einstein phase transition

From Carter's book Thermodynamics and Statistical Mechanics, the partition function of a bose-einstein gas in $d$ dimensions is $$ \ln(Z) = ...
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0answers
34 views

Making Pudding; A complicated non-equilibrium statistical process?

There are a lot of non-equilibrium processes examples given in physics literature. But some processes that are present in everyday life are not treated. As an example, the formation of pudding can be ...
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1answer
108 views

Conformal blocks in 2D CFTs

I have studied conformal field theories in two dimensions and I understand the basic idea behind conformal blocks too. But I never completely realized what they are when it comes to computing them. ...
2
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0answers
69 views

Topological order and entanglement in quantum quench problem

I would like to ask about useful reviews, must-read papers on the study of topological order and entanglement in quantum quench problems that give a good introduction to the topic.
2
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1answer
41 views

Ewald summation without repeating one particle periodically?

I need to perform an Ewald summation for a Brownian Dynamics simulation. In the normal Ewald summation procedure, all particles in the simulation box are periodically repeated in the neighbouring ...
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1answer
98 views

canonical ensemble that is quantum mechanical and continuous?

I do not understand what the following statements from Wikipedia mean For a canonical ensemble that is quantum mechanical and continuous, the canonical partition function is defined as $$ Z = ...
2
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1answer
69 views

Are Fermi-Dirac-statistics relevant to view the universal system of neutrinos?

Should the energy distribution of neutrinos be affected by Fermi-Dirac statistics? And if so, what would the consequences be? Could this locally cause weak interaction because of the Pauli Exclusion ...
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1answer
38 views

Mono-atomic gas particles coupled by spring forces don't care how many particles are involved?

I calculated the partition function of $N$ classical atoms of identical mass $m$ who all experience a mutual spring forces with identical spring constant $k$. The Hamilton is \begin{align} H = ...
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1answer
119 views

How to explain the Venturi effect with Kinetic Theory?

From a macroscopic perspective a fluid flowing through a pipe gets accelerated when the pipe's cross section gets narrower. According to $F= ma$ a force must be present to do this. This force is ...
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57 views

Maximizing particle annihilation of a certain particle type?

Is there any theoretical situation where one would be able to maximize the production of a certain type of particle? I wish to continue discussing this question: Where would dark matter be produced? ...