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

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93 views

How is $ \left(1-\frac{p^2}{2mE}\right)^{3N/2-2} =\; \exp\left(-\frac{3N}{2}\frac{p^2}{2mE}\right)\;?$ [closed]

How is $$ \left(1-\frac{p^2}{2mE}\right)^{3N/2-2} = \exp\left(-\frac{3N}{2}\frac{p^2}{2mE}\right)$$ (Karder, Statistical Physics of Particles, Page 107) in the large $E$ limit. Here $N$ is particle, ...
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1answer
81 views

Statistical mechanics of ideal gas in a box with adsorption states on surface [closed]

Assume we have a cubic box of side length 1m with ideal gas particles inside. We assume the binding energy of a gas molecule to the wall is 1eV. One can make the simplifying assumption that: ...
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0answers
140 views

on fundamental 2D conductivity equation boundary value problem

Consider the following homogeneous boundary value problem for a function/potential $u(x,y)$ on the infinite strip $[-\infty,\infty]\times[0,\pi/4]$ w/positive periodic coefficient/nductivity ...
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0answers
52 views

The energy density of states for a 2D electron gas [closed]

I am currently trying to solve for the electron density of states of an electron gas system restricted in 2D. I managed to find f(k)dk, the density of states with respect to the wave vector and i know ...
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23 views

Existence of statistical ensemble with fixed energy but varying volume

To me, every statistical ensemble in statistical physics was introduced beginning with the microcanonical ensemble, in which every microstate is equally probable. A canonical ensemble is described by ...
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1answer
126 views

What is entanglement entropy? and all those stories about counting [closed]

In Quantum mechanics entanglement is a concept that informs us about nature of states. It is a statement about non-product states, thus correlations. This is my rather foolish view of ...
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3answers
73 views

If an Ising model is in contact with two thermal reservoirs, would it still experience a phase transition if one of the reservoirs is below Tc?

For example; Two reservoirs are at each end of a one dimensional or even two dimensional lattice. One of the reservoirs has the temperature T < Tc. Would the lattice site have a phase transition ...
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2answers
80 views

Book recommendation for nonequilibrium thermo/stat mech

I'm doing an undergrad research project that lies at the intersection of biology and nonequilibrium thermodynamics, but I'm starting to realize almost none of my equilibrium thermo/stat mech knowledge ...
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59 views

What will a glass look like in 500 years?

The glass is in a metastable state. It is changing constantly. So what will a piece of glass look like in 500 years in room temperature?
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27 views

In stochastic thermodynamics, can you define the notion of equilibrium for microstates/individual trajectories?

Recently there has been quite some research on interpreting statistical thermodynamical quantities at the level of microstates/individual trajectories. Although I did not find any ...
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0answers
28 views

Spin interaction of Virtual Phonon's forming Cooper Pairs

Im confused about the spin of virtual Phonons, my lecture notes suggested that even spin bosons repel opposite charges, and it also suggested that cooper pairs form by considering the "Charge" to be ...
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1answer
83 views

“distinguishability” of 1D identical particles

Recently when I deal with 1D electron system, it occurred to my mind that since these electrons are not able to bypass each other during the scattering processes, we can actually label them as the ...
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1answer
179 views

Has there been any experimental verification of Jeremy England's theory of dissipation-driven adaptation?

In this paper, Jeremy England discusses about dissipation-driven adaptation, which proposes a mathematical explanation for the origin of life. While there is almost general consensus on the ...
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0answers
42 views

annealed randomness vs quenched randomness

what is meaning of annealed randomness and quenched randomness? in this article used this phrase to compare the model and earthquake data.
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1answer
130 views

What exactly is entropy? Why is it measure of randomness? [duplicate]

What exactly is entropy? Why is it measure of randomness? I have been told Entropy is measure of randomness and it increases everytime randomness increases. What is Randomness? Randomness in what? ...
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0answers
51 views

As the World Turns [closed]

Does the Earth's axis change with the magnetic reversal as it is taking place?
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1answer
165 views

Fermi's Golden Rule

Consider a system with countable quantum states. One can define $J_{ij}$ as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\sum_{i} ...
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1answer
70 views

Direction of time in an insulated room

I am puzzled with thought experiment that resembles/is version of Bolzmann's brain-hyphothesis. I could explain it in following way: Let’s assume that we have isolated system full of some stuff, ...
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1answer
35 views

Time dependence of density operator in quantum statistical mechanics

I'm struggling to understand a couple of textbook explanations relating to the density operator in quantum statistical mechanics. Firstly, in Huang's book "Statistical Mechanics" it says that "The ...
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1answer
136 views

Why is the logarithm of the number of all possible states of a system differentiable?

Temperature of a system is defined as $$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$ Where $\Omega$ is the number of all accessible states (ways) for the system. $ ...
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26 views

trying to figure out an expansion in Brownian motion derivation

In the derivation for the diffusion equation on the wikipedia article for Brownian motion, they have these equations: I can't figure out how $\rho(x+\Delta,t)$ gets expanded, though. For a Taylor ...
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1answer
49 views

Shear stress in cylindrical coordinates?

In cylindrical coordinates the momentum flux is given by (in the $r$ direction): $$ \Pi=-\eta \frac{\partial (r\omega)}{\partial r}$$ Where $\eta$ is the viscosity. Therefore one would expect that the ...
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1answer
36 views

What is the fraction of ionized hydrogen atoms under certain approximation

Given the ionization reaction $2H^0 <=> H^+ + H^-$ where: $H^+$ is the ionized state with electron occupancy n = 0 and energy 0 $H^0$ is the doubly degenerate neutral hydrogen atom with ...
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69 views

Deriving the Thermodynamic Beta

Pardon me if this question has been asked before. I'm an undergraduate student studying chemistry at the moment (specifically towards synthetic chemistry). Recently I've been trying to study ...
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53 views

Calculating Microcanonical Entropy in Molecular Dynamics

As a beginning, I am simulating Argon liquid at 94 K and characterising as it is done by the Rahman's first paper on Molecular Dynamics. After going through the first two chapters of Art of Molecular ...
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0answers
42 views

Derive statistical entropy from information entropy

I'm trying to compute the entropy of an Hamiltonian system with a fixed energy from the information entropy. Consider a random variable $X$ (state) to be uniformly distributed in a domain $\Omega$ ...
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1answer
89 views

Energy of classical ideal gas in the grand canonical ensemble

The canonical partition function for an ideal gas is $Z(N,V,\beta) = \frac{1}{N!} (\frac{V}{\lambda^3})^N$ where $\lambda = \sqrt{\frac{\beta h^2}{2 \pi m}}$ is the thermal De-Broglie wavelength. It ...
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59 views

Decoherence in the long time limit of density matrix elements

For a state $$ |\Psi(t)\rangle = \sum_{k}c_k e^{-iE_kt/\hbar}|E_k\rangle, $$ the density matrix elements in the energy basis are $$ \rho_{ab}(t) = c_a c^*_be^{-it(E_a -E_b)/\hbar} $$ How is it that ...
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2answers
40 views

RMS Speed of Gas Molecule for Polyatomic Molecules

Halliday in his book and also many people say that RMS speed, $v_{rms}$ is $\sqrt{\frac{3RT}{M}}$. However, he used this formula in showing that kinetic energy, $K$, is $\frac32kT$. but how about ...
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56 views

In an equilibrium of two systems, why is not true that $\frac{\delta S_{1}}{\delta N_{1}} = \frac{\delta S_{2}}{\delta N_{2}}$?

Why is not true that $\frac{\delta S_{1}}{\delta N_{1}} = \frac{\delta S_{2}}{\delta N_{2}}$ across two systems that exchange particles? It is true, instead, that $\frac{\delta F_{1}}{\delta N_{1}} = ...
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31 views

What creates multiplicity in counting the number of ways energy quanta can be distributed among a collection of atoms?

Say that I have $q$ energy quanta, which I intend to distribute among $N$ indistinguishable atoms in some collection. These atoms have no limit on the amount of quanta they can contain. Am I right ...
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1answer
115 views

Why is it so hard to explain that the Brownian Ratchet doesn't work?

The Brownian Ratchet stood up to a lot of scrutiny before it was finally shown why it would not work as a perpetual motion machine, but it seems weird to me that all of that was necessary. If the ...
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27 views

Explanation of example of ergodic movement

I was presented with the following question in as part of an introduction to ergodic movement: A man walks on a circle of radius 100 meters. Each man’s step is equal precisely 1 meter. There is a ...
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0answers
64 views

What is the meaning of thermal spectral function and thermal decay width in thermal field theory?

In Kallen-Lehmann spectral representation of 2-point correlation function \begin{equation} \langle 0|T\phi(x)\phi(0)|0\rangle=\int_0^\infty \frac{dM^2}{2\pi}\rho(M^2)D_F(x-y;M^2),\quad (a) ...
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1answer
85 views

Why is the number of distinct momentum states of a quantum particle moving in one dimension given as $\frac{L_p}{\Delta p_x}\;?$

I was reading multiplicity of monatomic gas where I got to know that it is proportional to the position space & volume space. $$\Omega \propto V\cdot V_p \;. $$ In order to find the constant of ...
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1answer
137 views

Why is the derivative of the Fermi-Dirac distribution negative?

Why the derivative of Fermi-Dirac distribution function at absolute zero temperature becomes negative of Dirac_Delta function. The Fermi-Dirac distribution function is \begin{equation} ...
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1answer
67 views

Sharpness of multiplicity function

This is quoted from Daniel Schroeder's An introduction to thermal Physics: $$\Omega= \left(\frac{e}{N}\right)^{2N} \; e^{N\ln (q/2)^2} e^{-N(2x/q)^2}\;=\; \Omega_\text{max} \cdot e^{-N(2x/q)^2}\;. ...
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29 views

Canonical and grand canonical partition function for Hamiltonian H= (N_1-N_2)^2

While preparing for my statistical physics exam I encountered the following problem: A quantum system consisting of two subsystems 1 and 2 is described by the following Hamiltonian: ...
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1answer
63 views

Maxwell Boltzmann distribution: Going from momentum to energy

I am learning about the Maxwell Boltzmann distribution, and am trying to convert the equation from momentum into energy, but I'm stuck on changing $d^n p$ into $dE$. I have the equation: $$ ...
3
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3answers
126 views

Physical distinction between mixing and ergodicity

How can one in a very contrasting manner distinguish between the physical meaning of mixing dynamics and that of ergodic dynamics? More precisely, is one a stronger condition than the other? (which ...
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2answers
327 views

Extending the ergodic theorem to non-equilibrium systems

I try to make this as short and concise as possible. For equilibrium systems in statistical mechanics, we have the Liouville's theorem which says that the volume in phase space is conserved when the ...
2
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1answer
85 views

Volume as a choice of measure in phase space

For equilibrium systems, we expect the Liouville theorem to hold. This theorem states that the density function of the states of the system is a constant of motion, which in turn can be translated ...
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0answers
42 views

Books on path integral methods [duplicate]

Are there advanced books on applications to physics of the method of path integral? I am aware of some of the standard textbooks on QFT, but looking for more advanced applications of the method.
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0answers
58 views

First law of thermodynamics with additional term

I read in a paper that a "known expression for the heat received by a body" is $$dQ=dU+pdV-\mathbf{v}\cdot d\mathbf{P}$$ where $\mathbf{P}$ is the linear momentum of the body, $p$ is the pressure, ...
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1answer
46 views

About bosonic, fermionic state in identical particles

The upper picture is my ideas which represent states by using the tensor product. but the lower picture, as you see, includes uppermost states. i don't know how to treat the uppermost states in lower ...
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0answers
59 views

Current status of nonextensive statistical mechanics

A version of the maximum entropy principle is the following. $$\max_{P}~~~ -\sum_i p_i\log p_i$$ subject to all probability distributions $P=\{p_i\}$ satisfying $$\sum_i p_i \epsilon_i = U.$$ ...
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86 views

How are the real-space RG transformations defined?

I'm reading Shang-keng Ma's book Modern theory of critical phenomena, and I'm a bit confused as to how the real-space RG transformations are defined. Ma basically says that these transformations are ...
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1answer
90 views

How to find the normalization constant of Fermi-Dirac distribution function?

The Fermi-Dirac distribution function is given by $$f(E):=\dfrac{A}{{\mathrm e}^{(E-E_{F})\,/\,(k_{B}T)}+1},$$ where A is the normalization constant. When we sum over all the states, we get $1$. ...
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1answer
57 views

What is a good software for Ideal Gas simulation?

I am looking for a software that simulates the microscopic behavior of an ideal gas, something like this: http://www.youtube.com/watch?v=tEFHkcx2cz0 (unfortunately this program is not openly ...
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1answer
111 views

Quantum mechanics and second law of thermodynamics

Recently I came across this idea of Gibbs that, it is the coarse-grained entropy that always increases, whereas the fine-grained remains a constant. So classically, coarse graining refuses us some ...