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

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Meaning of the phase space in statistical physics

I have a silly question about the phase space. I am confused with the meaning of points in phase space. Does the each point in phase space represent concrete particle of the system, or does it ...
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0answers
53 views

Question about Ginzburg-Landau Theory

I was reading CH3 of Reichl's "A Modern Course in Statistical Physics" on Ginzburg-Landau theory and don't really understand a couple of points he makes. He writes: I don't understand why the first ...
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1answer
86 views

What is the correlation between QFT and thermodynamics?

This may be a naive question. In physics many processes are symmetric, except a few involving entropy, or the arrow of time. Another one has to do with heat generation. We can generate heat, or energy ...
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2answers
71 views

What is the pressure that supports boson star?

What is the pressure that supports boson star? I noticed that for a Bose-Einstein condensate $$ p = k_BT\frac{g}{\lambda^3}\zeta(5/2) $$ where $g$ is the degeneracy and $\lambda$ is the thermal ...
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0answers
37 views

When does $E=\frac{3}{2}pV$ hold?

I only know that it holds for classical (monatomic) ideal gas and quantum ideal gas. But does it hold for interacting classical gas (e.g. van der Waals gas)?
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2answers
75 views

Experimental confirmation of the textbook explanation for local entropy reductions

Clarification: In my original wording of this question, regrettably, I did not make it clear that I am interested in the the Boltzmann/Gibbs/statistical (BGS) interpretation of it, as opposed to the ...
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0answers
19 views

Equilibrium states for the Curie-Weiss-Potts model and large deviations

I am doing a project in Large deviation theory applied to statistical mechanics and I was reading this paper http://arxiv.org/abs/cond-mat/0410744. For the general setting we start with a finite ...
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1answer
22 views

Average speed of a molecule in a fermion gas

Starting from Fermi-Dirac statistics, how can be calculated the average speed on the x-axis, $\langle v_{x} \rangle$, of a molecule in a fermion gas a $T= 0\ \mathrm K$?
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1answer
75 views

Relation between master, Fokker-Planck, Langevin, Kramers-Moyal and Boltzmann equations

I'm looking for the relation between four important equations which we study in stochastic processes in physics. These equations include Master, Fokker-Planck, Langevin, Kramers-Moyal and Boltzmann. ...
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0answers
32 views

How is zonal flow defined and computed?

The transition to turbulence in pipe flow was recently observed to be in the same universality class as directed percolation. This was done by reinterpreting the turbulence and laminar flow in terms ...
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0answers
39 views

Diffusion of carbon monoxide in air

I have been reading about carbon monoxide online. It is lighter than air; Yet, in the case of fire, most online sources claim it spreads evenly throughout a room. Why is this the case? How is it ...
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0answers
28 views

Temperature dependent chemical potential

Chemical potential is determined by the number of electrons in the system and coincides with the Fermi energy at zero temperature. The chemical potential can shift as temperature changes if the ...
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1answer
74 views

Why thermal conductivity increases with temperature?

what is the molecular mechanism with which thermal conductivity increases by increasing temperature? at least for metals? I know that heat increases the oscillations of the atoms in the crystal. But ...
58
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1answer
8k views

If we had a “perfectly efficient” computer and all the energy in the Milky-way available, what number could it count to?

The idea for this question comes from an example in cryptography, where supposedly 256-bit symmetric keys will be enough for all time to come (brute-forcing a 256-bit key is sort-of equivalent to ...
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2answers
173 views

Do gravitational waves have entropy?

We know, according the current understanding of black holes and General Relativity, as well as quantum fields in General Relativity, that black holes have an entropy proportional to the area of the ...
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1answer
51 views

Fermi energy of electron gas with electrostatic interaction

I have been given the following exam question and am unsure how I would go about solving it: Consider the case of a one-dimensional metal, consisting of a chain of $N$ positive charges $+q$ ...
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1answer
63 views

Noise spectrum of the thermal noise?

If we have a thermal noise generated by Brownian stochastic force $\xi (t)$, it has zero mean value. And its correlation function at temperature T is : \begin{equation} \langle\xi(t) \xi(t^{\prime})\...
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2answers
82 views

Modern textbook on statistical field theory

What is a good textbook on statistical field theory, with an emphasis on applications to non-equilibrium phenomena? I am a final-year undergraduate, have already taken introductory classes in ...
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1answer
56 views

Velocity from the cumulative distribution function of the Boltzmann distribution

I want to get a Boltzmann distribution of the $v_x$, $v_y$ and $v_z$ velocity components (please, notice that the distribution is one-dimensional). To do so, I need the cumulative distribution ...
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0answers
60 views

Which condition is stronger - ergodicity or mixing?

Reading a statistical physics book, I've encountered the following assertion (without further explanations): [..] the presence of dynamical instability makes the trajectory of a system much more ...
5
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1answer
247 views

Calculate the entropy per atom in Bohmian Mechanics

Bohmian mechanics description of a large number of interacting atoms would require a large phase space due to the large number of classical degrees of freedom. The entropy per atom is given as the ...
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1answer
51 views

Gibbs' Free Energie

What terms are needed to consider to create a rabbit out of nothing and place it in the classroom? Does this caption answer the question?
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2answers
94 views

Understanding Gibbs $H$-theorem: where does Jaynes' “blurring” argument come from?

According to this Wikipedia article, the $H$-theorem was Boltzmann's attempt to demonstrate the irreversible increase in entropy in a closed system starting from reversible microscopic mechanics. ...
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2answers
81 views

Maxwell velocity distribution, in 1D or otherwise

I learned from my textbook that Maxwell's velocity distribution gives: $$v_{rms} =\sqrt{\frac{3kT}{m}}$$ $$v_{avg} = \sqrt{\frac{8kT}{\pi m}}$$ Presumably this is for a three dimensions. This confuses ...
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0answers
49 views

Hindered rotation model for flexible polymers: deriving the Flory characteristic ratio

In the hindered rotation model we assumes constant bond angles $\theta$ and lengths $\ell$, with torsion angles between adjacent monomers being hindered by a potential $U(\phi_i)$. In Rubinstein's ...
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0answers
30 views

A micro-reversible stochastic process that models transitions between states with variable energies

Suppose we have a system with 3 possible states A, B and C (there could be $n$ states as well) with energies $E_a(t)$, $E_b(t)$ and $E_c(t)$ that vary with time. If our system has a constant finite ...
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1answer
49 views

Why is the average thermal velocity 0?

Thermal velocity is the velocity of the free electron due to their random motion. So how is the average value 0?
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1answer
27 views

Example of a Carnot machine made of a different physical system than a ideal gas?

Anybody knows an example of a Carnot machine made with any different thing than a gas? For example wire or a magnet. I was wondering that since I read the Kardar's book on Statistical Mechanics. He ...
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1answer
40 views

What is the difference between these two expressions for the partition function, Z?

What is the difference between these two expressions given for the partition function, Z? $$Z = \sum_{i}e^{-\varepsilon_i/kT}$$ $$Z = \sum_{j} g_je^{-\varepsilon_j/kT}$$ where each energy level has ...
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0answers
18 views

Triangular and Kagome lattice anti ferromagnet at zero temperature

The triangular lattice with anti ferromagnetically coupled nearest neighbour ising spins has a power law ordered zero temperature state at the three sublattice wavevector. Kagome lattice, with the ...
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0answers
17 views

Fermi-Pasta-Ulam for the beam equation

The Fermi-Pasta-Ulam numerical experiment is based upon the discrete wave equation, with a small non-linearity added to the forcing term. Does anybody know of similar research performed on the beam ...
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6answers
6k views

Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms tries ...
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1answer
68 views

Poincare recurrence time of the Universe

I've read around a bit, and it seems to be universal that the notion of a Poincare recurrence time for the universe exists. And it seems to be debated that the universe can be given an entropy, as it ...
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4answers
108 views

Is it possible for a system to become irreversible?

Imagine a ball bouncing in a box for a long time. We know, there is a certain path it can go to bounce off infinitely (see the image). If it gets to this state, it will never be able to get back again....
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70 views

Time Scales Of Processes In Molecular Dynamics

Suppose I run a molecular dynamics simulation of a fluid sandwiched between solid walls which are periodic in the lateral directions and finite in the direction of the fluid film thickness. Now, I ...
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1answer
84 views

boltzmann weight factor and statistical ensembles

i am working on a project about in-equivalence between statistical ensembles ( micro-canonical and canonical to be more precise ). how can we show that the in the canonical ensemble the system is ...
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0answers
18 views

How to show a ratio of probabilities in Boltzmann statistics from entropy?

Consider a system in a state $s$ of energy $E(s)$ in thermal equilibrium with a reservoir of energy $U_R$, volume $V_R$ and number of particles $N_R$. The ratio of probabilities of being in states $...
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3answers
38 views

Why only $x$-component of gas particle changes when it strikes with wall perpendicular to $x$-axis elastically?

In my book ''Ncert Class 12" It is written We begin by considering the collision of one molecule with one of the walls of the container, oriented with a unit normal vector pointing out of the ...
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1answer
26 views

Statiscal treatment of multiparticle system (Thermodynamics) [closed]

If a system of two energy levels with energies $\epsilon_1$ and $\epsilon_2$ is populated N particles at temperature T. The degeneracy of both levels is one. The particles populate the microstates to ...
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0answers
27 views

Susceptibility at a first-order phase transition

I have two questions about first-order phase transitions: 1) is the susceptibility divergent at a first-order phase transition? 2) if yes, does it diverge in a universal way as in continuous phase ...
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0answers
30 views

Functional Gaussian Integral Involving Gradient Square with non-trivial Kernel

I have been trying to solve the following functional gaussian integral. I've had problem finding the inverse kernel. $f(x)$ and $\rho(x)$ are two known scalar fields and they do vanish at infinity. $...
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3answers
132 views

Does entropy always increase with temperature? [duplicate]

For any system can we always say that entropy increases with temperature. In other words: $$\left(\frac{\partial S}{\partial T} \right)_{\{\alpha\}}\ge0$$ where $\{\alpha\}$ is the set of parameters ...
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1answer
24 views

Why do we have this difference in the multiplicity of Cartesian space and momentum space for a gas?

For an ideal gas, the multiplicity of an ideal gas with $N$ molecules in Cartesian space is $$\Omega_{\text{space}}=\Big(\frac{V}{(\Delta x)^3}\Big)^N.$$ This is pretty intuitive, because we are ...
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1answer
133 views

Obtaining the temperature from Bose-Einstein and Fermi-Dirac distribution

Lets say you are given a distribution function $f(p)$ and you want to define a temperature, $T_f$, for this distribution. (I assume $\mu = 0$.) It is then natural to define a temperature the ...
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1answer
73 views

Is there anything comparable to many-body localization in classical physics?

I've only just started looking into many-body localization, so this question may come off as a little vague. But my understanding is that it relates to how some quantum systems do not thermalize, as ...
6
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2answers
82 views

The calculation of the entropy of a single atom

I used to think that the entropy of a single atom could not be calculated, for in my mind only the entropy of a system containing many atoms could be calculated. But my professor told me the entropy ...
3
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1answer
62 views

If Black holes are maximal entropy how can they evaporate?

According to Hawking/Bekenstein a black hole represents the highest amount of entropy for a given volume, (actually the entropy is related to the surface area of the black hole but the fact that they ...
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89 views

Entropy always increases in a closed system - what if the universe is open?

An interesting question I was asked: Entropy always increases in a closed system - what if the universe is open? Does that mean that entropy can decrease in such a system? Of course, I think there is ...
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16 views

Rugged Energy Landcapes (Free Energy vs Potential Energy Questions)

A spin glass has what is called a "rugged energy landscape." That is, when you cool down below a certain temperature, the system divides into many wells, all corresponding to slightly different ...
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31 views

How do inverse of Kirchoff matrix of a polymer possess the information for its mobility?

In Normal Mode Analysis of polymers like proteins, I have seen that mobility (measures like root mean squared fluctuations) can be found from the eigen values and eigen vectors of inverse of Kirchoff ...