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

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How do you measure numerically the central charge of a system?

Let's say that you are doing some Monte-Carlo simulations of a statistical system on a lattice and you observe scale invariance, meaning that you are at a conformal point. Can you get a numerical ...
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3answers
90 views

Problems with units of entropy in statistical thermodynamics

The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles ...
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0answers
45 views

Molecular simulation - Lennard-Jones potential [on hold]

For 2 atoms separated by a distance $r$, the potential function is given by $$u(r) = 4\epsilon [ (\sigma/r)^12 - (\sigma/r)^6]$$ (Lennard-Jones potential). Give the equation that define how pressure ...
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0answers
38 views

probability of sequence for given rate constants

lets consider a copolymer, $C_{r,s}^A$ containing r number of A monomers and s number of B monomers with A at the reactive end of the polymer. The equilibrium constant for A-A, A-B, B-A, and B-B bonds ...
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1answer
71 views

Proof of Loss of Lorentz Invariance in Finite Temperature Quantum Field Theory

In the standard quantum field theory we always take the vacuum to be a invariant under Lorentz transformation. For simple cases, at least for free fields, is very simple to actually prove this. Now ...
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8answers
1k views

What is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
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1answer
39 views

Grand partition function of gas of non-interacting spin-1 bosons in magnetic field

Consider a gas of non-interacting spin 1 bosons in a uniform B field, each subject to a Hamiltonian of the form: $ H(\vec{p},s_z) = \frac{p^2}{2m} - \mu_0 s_z B$ where $s_z$ can take the three ...
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1answer
106 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 ...
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0answers
46 views

Use of Boltzmann over Maxwell distribution

Why is the Boltzmann distribution used over the Maxwell distribution in many cases such as the derivation of Plancks law of thermal radiation, derivation of Einstein A and B coefficients, Langevin ...
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1answer
48 views

Canonical ensemble, energy, heat bath

I am studying through the book Thermodynamics and Statistical Mechanics by Walter Greiner and I’ve got a couple of doubts when I was reading about the classical ensembles, specially the Canonical ...
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2answers
51 views

Dimensionless entropy interpretation

Measuring temperature in joules instead in the artificial units of Kelvin would render entropy as a dimensionless quantity. This is quite appealing since entropy has always been quite a misterious ...
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2answers
341 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 ...
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2answers
106 views

General Thermodynamic equation of state

I heard my professor saying that the equation $$ PV = \frac{2}{3}U $$ is valid for any non-relativistic gas, be it Ideal or Real gas(includes quantum ideal gases). Is this true, If it is how can we ...
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3answers
208 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 ...
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1answer
42 views

Resources on Master Equations

Presently I am reading about "Introduction to dynamical process theory and simulation" which uses the notion of Master Equations to solve Markov process. I am very new to this. Can someone provide me ...
4
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1answer
152 views

Semi-conductors

Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states. I'd like to know why the mean number of excited electrons takes the form $$\bar n={N\over ...
2
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1answer
128 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
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1answer
48 views

The Equation of State for a Degenerate Fermi gas

I have read in Chandrasekhar's paper The highly collapsed configurations of a stellar mass Appendix I the equation of a degenerate Fermi gas as follows: $$n=\frac{8\pi}{h^3}\int^{p_0}_0 p^2dp$$ and ...
2
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1answer
51 views

Numerical Ising Model: Swendsen–Wang algorithm, Percolation theory?

When you look at the original paper of Swendsen and Wang in 1987: "Nonuniversal critical dynamics in Monte Carlo simulations" it is somewhat mentioned that the proposed algorithm uses percolation ...
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1answer
162 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 ...
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2answers
40 views

What materials are used in non thermal plasma?

While reading about non-thermal plasmas, I came across their ionization potentials(~1%), and other capabilities, such as their non Maxwellian energy distributions. At what temperatures, and pressures ...
2
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1answer
86 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 ...
5
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0answers
84 views

Fluctuation interaction between two uncharged spheres

I'm trying to figure out quantitatively what is the force, acting between two uncharged conducting spheres and I've got stuck. It is not a kind of homework - it is just a simple act of curiosity. I'd ...
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3answers
475 views

Why the temperature is getting lower when the universe is expanding

As we know, if an ideal gas expands in vacuum, as its energy is unchanged, the temperature remains the same. An ideal gas's energy does not depend on volume. In general, the energy is $kT$ times the ...
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0answers
34 views

Finding the moments of the Boltzmann/Gibbs Distribution

I am trying to compute the moments of the Boltzmann distribution using a moment generating function, by taking the Fourier transform of the distribution and then taking derivatives to find the ...
3
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1answer
97 views

Entropy of a two-level system

Consider a two-level system with energies and degeneracies $\epsilon_0 = 0, g_0=1$ and $\epsilon_1 = \epsilon, g_1=4$. I can show that the temperature at which both levels are equally populated is ...
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3answers
1k views

Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
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2answers
272 views

Fermi-Dirac Statistics

In Fermi-Dirac statistics the probability of being in a certain energy state is $$f(E) = \left[1 + \exp\left(\frac{E-E_F}{k T}\right)\right]^{-1}$$ In the area that I'm looking at the texts always ...
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1answer
48 views

A formula for the photon gas correlation function

i need to derive a formula for the photon gas correlation function $\left\langle\partial n_i\partial n_j\right\rangle $ where $$\partial n_i=n_i -\left \langle n_i \right \rangle.$$ whilst solving ...
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1answer
284 views

How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...
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1answer
56 views

Time homogeneous Markov chain for Axelrod's model

I am reading paper Axelrod's model of dissemination of culture , I am unable to understand the transition probabilities of time homogeneous Markov chain for this model. Can some one please explain it ...
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0answers
41 views

What excactly is a “fourier component of a density fluctuation”?

Light scattering texts say depending on the scattering angle, you are seeing a certain fourier component of a density fluctuation. This density fluctuation varies sinusoidally due to Brownian motion ...
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2answers
939 views

Temperature of a neutron star

In our everyday experience termperature is due to the motion of atoms, molecules, etc. A neutron star, where protons and electrons are fused together to form neutrons, is nothing but a huge nucleus ...
14
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1answer
148 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each ...
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0answers
47 views

How to numerically solve a complex equation? [closed]

I want to know that if you are given a very complex equation g(x)=A(T). How could you solve for x, which is a function of variable T. To be more specific, I encounter a polylogarithmic function I need ...
2
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3answers
585 views

Why is Avogadro's law always true?

Why is Avogadro's law always true? How and why do equal volumes of gases at equal pressure and temperature contain equal number of molecules? I know it is a fundamental principle in chemistry but I ...
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0answers
49 views

What algorithms can be used to compute the binodal in a ternary Flory-Huggins theory?

What are the most popular algorithms used to obtain a binodal curve for the ternary mixture (starting from Flory-Huggins theory)? I would like to obtain a plot similar to the one calculated here ...
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1answer
40 views

Which function denotes the energy of thermal motion within a system?

In thermodynamics, the heat $Q$ is defined as a type of energy in transfer, and is not a state function, which function denotes the energy of thermal motion within a system? 1) $TS$, (there is a ...
3
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0answers
35 views

Partition function of classical quadrupole in an electric field

The partition function of a dipole in an electric field is a well-known problem, analytical solvable (nice integral, can be calculated with pen and paper), for example in the Langevin treatment of ...
3
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0answers
64 views

Why is there a 'loophole' in Mermin Wagner for rotations?

I'm just starting out in my mathematics career by looking at some simple stuff on broken symmetries in statistical mechanics. Since 3D is 'hard' it would be very nice to look at 2D toy models of ...
4
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4answers
299 views

Mathematical proof of the Second Law of Thermodynamics [duplicate]

Is there some book or paper that formalizes statistical mechanics, like some people have done with relativity, and proves the second law of thermodynamics from more foundational axioms?
2
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2answers
62 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 ...
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2answers
221 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 ...
6
votes
3answers
209 views

Why is the Gibbs Free Energy $F-HM$?

With magnetism, the Gibbs Free Energy is $F-HM$, where $F$ is the Helmholtz Free Energy, $H$ is the auxiliary magnetic field, and $M$ is magnetization. Why is this? Normally, in thermodynamics, we ...
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1answer
48 views

Why does nuclear matter tend to maximize pressure?

I'm reading a text about equations of state of dense nuclear matter. It is often stated that the phase with maximum pressure is preferred. Why is that?
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6answers
707 views

How do you prove the second law of thermodynamics from statistical mechanics?

How do you prove the second law of thermodynamics from statistical mechanics? To prove entropy will only increase with time? How to prove? Please guide.
4
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1answer
59 views

What is an intuitive explantion for the fact that the Maxwell-Boltzmann distribution of energies is independent of mass?

If you take the Maxwell-Boltzmann distribution of velocities (which depends on the mass) and substitute $v=\sqrt{\frac{2E}{m}}$ you get the distribution for the energies, which turns out to be ...
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2answers
65 views

Phase space derivation of quantum harmonic oscillator partition function

I would like to derive the partition function for the quantum Harmonic oscillator from scratch: $$\tag{1} Z = \int dp \, dx\, e^{-\beta H}.$$ The free particle appears in many textbooks. $H = ...
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1answer
98 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 ...
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0answers
20 views

How to calculate the partial entropy in a fully connected ising system

I'm trying to reproduce a calculation that should lead to the partial entropy in a fully connected ising model for the high-temperature range ($\beta < 2$) in the thermodynamic Limit ($N ...