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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0answers
44 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 ...
2
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0answers
45 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
36 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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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 ...
6
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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 ...
6
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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
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 ...
2
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1answer
47 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 ...
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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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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 ...
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 ...
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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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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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
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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2answers
938 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 ...
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 ...
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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 ...
2
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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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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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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 ...
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0answers
17 views

Molecular field meaning in Liquid Crystal Theory

Given the Frank-De Gennes free energy $F = \int f(\boldsymbol{p},\nabla\boldsymbol{p}, ...)\ d\boldsymbol{x},$ for liquid crystals (see De Gennes-Prost, p. 107, formula 3.21), the vector ...
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1answer
84 views

Can statistical mechanics explain the second law completely? [duplicate]

Statistical mechanics is restricted to the postulate of the equal a priori probability, but this postulate does not need to be considered for thermodynamics, so the valid ranges of statistical ...
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1answer
46 views

What is the relation between entropy and mass of black hole?

What is the relation between entropy and mass of black hole? And what is the relation between symmetry of physics operation and entropy?For instance,measuring or doing measure on state of quantum ...
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1answer
32 views

Thermal Velocity

What is thermal velocity? What is it's physical significance? Wikipedia says: The thermal velocity or thermal speed is a typical velocity of the thermal motion of particles which make up a gas, ...
4
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0answers
46 views

Help with deriving an asymptotic expression

Note: I don't know if this is the best place for this question, because it is very specific. However, I'm not sure of a better place to go (apart from one of the other SE's). If you have a ...
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3answers
145 views

Why is Entropy's Definition Useful?

I have somewhat of an understanding for other physical quantities, but as far as entropy goes I only know it to be "disorder". Why is the change in entropy formula an appropriate/useful definition, ...
1
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1answer
48 views

Proof of Liouville's theorem: Relation between phase space volume and probability distribution function

I understand the proof of Liouville's theorem to the point where we conclude that Hamiltonian flow in phase-space is volume preserving as we flow in the phase space. Meaning the total derivative of ...
4
votes
2answers
158 views

Counting Problems in Physics

What are some classic counting problems in physics? I'm trying to think of interesting examples to give in a math class on the matter, and I feel as if physics should have some ones to offer.
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2answers
46 views

Correlation in electron gas

In the textbooks that I read (namely Ashcroft/Mermin , Marder, etc.) it seems that a distinction is made between the correlations in electron gas and a Couloumb interaction between the electrons. What ...
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2answers
45 views

Thomas - Fermi screening

I read in Ashcroft & Mermin's Solid State text that for the Thomas-Fermi approximation to be applicable, the external potential needs to be "slowly varying," What does it mean for a function (in ...
2
votes
3answers
85 views

Is thermodynamic free energy and potential energy the same thing?

The equation for free energy $F$ and potential energy $E_{pot}$ are: $$ F=U-TS \\ E_{pot} = E_{tot} -E_{kin} $$ But the temperature $T$ is proportional to the average kinetic energy of a system. So ...
1
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0answers
59 views

Ergodic Hypothesis; canonical ensemble

I'm currently studying for an exam in thermodynamics/classic statistical mechanics and 2 things came up which are confusing me. First the ergodic hypothesis states that it is equal to take the mean ...
8
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2answers
159 views

What conditions do a bunch of atoms need to satisfy to have a temperature?

What conditions do a bunch of atoms need to satisfy to have a temperature? Suppose that we have a beam of helium atoms travelling in a common straight line, equally spaced with the same velocity. If ...
5
votes
1answer
78 views

Is there any model in statistical physics which has the ratio of specific heat exponent to correlation length exponent, $\alpha/\nu \approx 2.44$?

I am simulating a disordered ising-like model in 2d whose phase transition is expected to be continuous, whose universality class is as yet unknown. By plotting the Specific heat scaling function, ...
4
votes
4answers
298 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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0answers
41 views

Statistical Mechanics with Gravity [closed]

What complications arise when examining the statistical mechanics of a system under the influence of gravity? Is it significantly different from the classical treatment of statistical mechanics?
0
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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 ...
3
votes
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 ...
2
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0answers
37 views

Why does decay of correlations imply absence of order?

In a few articles I have read, a two-point correlation function $\langle g(x)g(y) \rangle$ is shown to decay with increasing distance of $x$ and $y$, and this is then taken to imply an absence of the ...
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0answers
24 views

Methods for quantifying a network of coupled oscillators

I usually am more on the statistics part of things, so pardon my misuse of the terminology. I am simulating a network of non-pulse coupled non-linear oscillators ( I am not sure what the correct term ...
0
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0answers
31 views

Wolff vs Swendsen Wang Algorithm

Following the orginal paper of Swendsen Wang, their dynamical critical exponent $z$ is about $z=0.35$, whereas the Wolff Algorithm seems to have $z=1.19$. When I calculate the Correlation time though, ...
3
votes
3answers
183 views

Existence of negative temperatures and the definition of entropy

How negative temperatures can be possible has been treated on StackExchange before (several times in fact), but in light of some recent academic discussion, most of these answers seem to be possibly ...
3
votes
3answers
143 views

In what limit do we *really* get Maxwell-Boltzmann statistics from Bose-Einstein and Fermi-Dirac?

Fermi-Dirac and Bose-Einstein energy occupation number $n(\epsilon)$ in natural units ($[T]=[\epsilon]$) read $$n(\epsilon) = \frac{D(\epsilon)}{e^{(\epsilon-\mu)/T}\pm 1},$$ where $D(\epsilon)$ is ...
4
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1answer
161 views

What's the most fundamental definition of temperature?

What's the most fundamental definition of temperature? Is it the definition concern about average energy, number of micro states, or what? By "fundamental", I mean "to be applied" in such general ...