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

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19 views

Why is energy minimized over the string landscape?

As understand it, the 4D string landscape is a function that assigns an energy to every possible compactification of the 6 small spatial dimensions. We expect our universe to lie in a local energy ...
0
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4answers
26 views

Are elements of statistical ensemble fixed or dynamic?

I will use the simplest example I can think of to explain what I am trying to understand. Consider a system with ~$10^{23}$ particles in an equilibrium with fixed values of pressure, volume and ...
3
votes
1answer
21 views

Why is the molecular partition function only broken down into translational, rotational, vibrational, and electronic states, ignoring configurations?

Per Atkins and others, energy is the sum of contributions from the translational, rotational, vibrational, and electronic modes of motion. Since the formula for the partition function is $Q=\sum_i e^{\...
5
votes
2answers
211 views

Is ergodic hypothesis in contradiction with the notion of equilibrium?

From wikipedia: In physics and thermodynamics, the ergodic hypothesis1 says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the ...
1
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1answer
22 views

Relation between Pair Correlation Function and Static Structure Factor

I am currently looking to calculate the static structure factor of a computer-generated sphere packing I have been referring this paper as well as numerous other online sources to try and understand ...
0
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1answer
71 views

Physicists use of “Information” [on hold]

this is a philosophical question for physicists to answer. Elsewhere here on physics.se I learned that "information contained in a physical system = the number of yes/no questions you need to get ...
3
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0answers
63 views

Proving that the Boltzmann entropy is equal to the thermodynamic entropy

I've been trying to understand how we can equate the Boltzmann entropy $k_B \ln \Omega$ and the entropy from thermodynamics. I'm following the approach found in the first chapter in Pathria's ...
0
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0answers
21 views

Can Fluctuation-Dissipation Theorem Apply to Magnetic Forces in Multi-Spin Systems

Let's say I have multiple spin systems (atoms in a protein) in a solution of water and the spin systems are all producing a magnetic field $\mathrm{B_{loc}}$ that affects nearby spin systems. Will the ...
0
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0answers
19 views

Proof of Exponential Decay Behavior of Time Correlation Functions

For a given protein, I know that the NMR Spectroscopy magnet generates a field $\mathrm{B_o}$ and that the interactions with the spins in the local environment generates a much smaller field $\mathrm{...
0
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1answer
33 views

Problem with simulation STP Temperature Measurement Ideal Gas Program in Tobochnik [closed]

The simulation I am considering is provided here. (In case the link no longer works, the program is called 'STP Temperature Measurement Ideal Gas Program' and the homepage of the website is here. ...
2
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0answers
24 views

Is the free energy density analytic in temperature at the Kosterlitz-Thouless phase transition?

I know that the KT transition is infinite-order so the free energy density is a smooth (i.e. infinitely differentiable) function of temperature, but is the function actually analytic at the critical ...
0
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0answers
16 views

How to estimate the phase diagrams ($d=2$) using the renormalization method (Migdal-Kadanoff)? [closed]

How can I establish the phase diagrams using the Renormalization group method (Migdal-Kadanoff)?
0
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0answers
13 views

Maxwell's distribution analogue for angular velocity

Consider hydrogen ($\mathrm{H_2}$) as an ideal gas. We know that distribution of translational velocities is given by Maxwell's distribution. However our gas is diatomic, which means every molecule ...
27
votes
5answers
2k views

Why does a critical point exist? [duplicate]

I still cannot fully comprehend the essence of a critical point on phase diagrams. It is usually said in textbooks that the difference between liquid and gaseous state of a substance is quantitative ...
1
vote
1answer
53 views

The relation between critical surface and the (renormalization) fixed point

In the book, I read some remarks about the criticality: Iterations of the renormalization (group) map generate a sequence of points in the space of couplings, which we call a renormalization ...
5
votes
2answers
93 views

number of states in microcanonical ensemble

I have a problem with the definition of $\Omega(E,V,N)$ — the number of microstates with $V$, $N$ and energy $E$. It starts with the definition of the PDF. If one defines the PDF as follows: $...
0
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0answers
23 views

The two point fluctuation autocorrelation function in computing the scattering intensity?

In this paper: http://www.pnas.org/content/113/8/2029.full.pdf?with-ds=yes and: http://www.pnas.org/content/113/8/2029.full.pdf The authors try to compute the scattering intensity for a simulation ...
1
vote
1answer
54 views

Rotation of superfluid

I have two questions related to rotation of superfluids. Firstly, what is the main reason that superfluid cannot rotate as a whole object ? (I found that it is true in Landau's Statistical Physics but ...
0
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0answers
36 views

change in entropy constant V proof

In the justification above it is noted that dV=0 througout the process. They use the macro formula dU=TdS. How can they use this formula when dV=0 hence pV=nRT gives $$T(p)=\frac{V}{nR}p=kp$$ I mean ...
2
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0answers
24 views

What is the significance of the assumption of “full energetic degeneracy” in this paper?

I'm reading the new paper "Foundations of statistical mechanics from symmetries of entanglement" (available on arxiv), in which the authors Deffner and Zurek note that the quantum microcanonical state ...
5
votes
0answers
57 views

Are second-order phase transitions always scale/Lorentz invariant?

I know that both scale invariance and Lorentz invariance typically emerge at second-order phase transitions, but is there a proof or a counterexample? (I know that it's believed that any theory that ...
0
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0answers
24 views

Quantum coherence as a thermodynamic quantity

Now that we know quantum coherence is one kind of resource that can be measured, is there any chance we can find some relation between quantum coherence and macroscopic thermodynamic quantity, just ...
5
votes
0answers
113 views

Computational scaling of quantum and classical Monte Carlo algorithms

How does the computational complexity of finding an equilibrium thermal state for a given Hamiltonian at a given temperature scale with system size under classical and quantum Monte Carlo? I know ...
0
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0answers
17 views

Hydrogen bonding and dichotomous Markov process

The hydrogen bonding function between water and monomer (from a micelle/bilayer) can be defined as $h(t) = 1$ if the hydrogen bond exists between the two and $h(t) = 0$, if there is no hydrogen ...
0
votes
1answer
66 views

A question from CFT (possibly due to the English expressions)

I am currently reading the book ''Conformal Field Theory'' and encountered a description about which I am very confused. I am afraid to say, this may be due to the fact that I am not a native English ...
1
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0answers
24 views

Reference: authoritative reference on Gibbs and Boltzmann's entropy

Can someone reference a good, standard textbook on thermodynamics or quantum mechanics that explicitly states the formula for Gibbs and Boltzmann's entropy (or maybe Shannon as well)? I am asking ...
1
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0answers
41 views

Liouville's theorem and systems in equilibrium

This is related to a statement I once came across in Reif, that systems in equilibrium, described by the micro-canonical ensemble,stay in equilibrium. In the appendix(pg 628), he asserts that, in a ...
0
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0answers
35 views

About Kardar's Statistical Mechanics Textbook

I am confused by Kardar's convention in Statistical Mechanics of Particles. In Kardar's discussion about canonical ensemble, he uses the probability and sum rather than PDF and integral. But the phase ...
0
votes
0answers
20 views

Eigen energy of the Landau levels in a tilted magnetic field

The problem pertains to a fermi gas in a tilted magnetic field confined by a harmonic potential in the z direction. I chose the vector potential $(0,ax-bz,0)$. I obtain the following hamiltonain with ...
0
votes
0answers
24 views

Applications of exponential family Markov random fields in statistical physics

Ising model and its relatives are popular in statistical physics. Are there any physical systems that can be characterized by exponential family Markov random fields (e.g., the one in http://arxiv.org/...
2
votes
1answer
50 views

What is the relation between the Boltzmann distribution and Boltzmann equation?

The Boltzmann equation without collision operator $\Omega$ is as follows: $$\dfrac{\partial f}{\partial t} + \mathbf v \cdot \nabla f = 0 \tag{1}$$ Where $\mathbf v$ is the velocity, and $f$ is the ...
-2
votes
0answers
18 views

How are the charges on the plates of a capacitor distributed?

Given a specific overall amount of energy a rectangular parallel plate capacitor stores what number of atoms on a specific plate would have any given specific charge?
1
vote
1answer
29 views

The expression of the density in terms of molecular mass and the distribution function

I am reading a book about the boltzmann equation, the author gives the expression of the fluid density $\rho$ as follows: $$\rho(\mathbf r,t) = \int {M\,f(\mathbf r,\mathbf c,t) \, \mathrm d\mathbf c}$...
4
votes
2answers
118 views

How to derive entropy from density of states?

I'm trying to derive the entropy of a black hole, given the density of states of a bosonic string (the details are not relevant). The density of states is $$ \omega(E) = E^\alpha e^{\beta E} $$ The ...
4
votes
2answers
135 views

What is the black hole information paradox really? [closed]

Preliminaries What is the black hole information paradox really? Is it a sophisticated way to ponder and debate the existence of an operator on the boundary that can tease out the interior of a ...
0
votes
2answers
60 views

Relation between entropy and internal energy

I am confused as to what is the relation between entropy and internal energy. Entropy is always presented as a measure of the randomness in a system. So when we supply heat to a well insulated system ...
5
votes
0answers
46 views

Is there a block spin renormalization group scheme that preserves Kramers-Wannier duality?

Block spin renormalization group (RG) (or real space RG) is an approach to studying statistical mechanics models of spins on the lattice. In particular, I am interested in the 2D square lattice model ...
0
votes
1answer
57 views

What is the relationship between Maxwell-Boltzmann statistics, Boltzmann distribution and Maxwell-Boltzmann distribution? [closed]

I have recently been studying some statistical thermodynamics and I am currently trying to understand all the different concepts of the course. I was wondering about differences between MB statistics, ...
3
votes
0answers
25 views

Multi-Cut Matrix Models

I have a question pertaining specifically to a one-matrix model with a multi-cut solution. The standard procedure is to take a polynomial superpotential $W(x)$. In the classical limit (analogous to $...
1
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0answers
24 views

Video lectures for studying graduate level kinetic theory

As the title says it all, I require Video lectures for studying graduate level kinetic theory including but not limited to detailed analysis of viscosity and conductivity, diffusion and Maxwell's ...
2
votes
0answers
32 views

Specific heat of water

In statistical mechanics, we derive all the thermodynamic quantities, including specific heat $c_v$ from the partition function $Z = \mathrm{Tr} \, [ \, e^{\beta H } \,]$ . For solid, we assume simple ...
5
votes
2answers
62 views

Books on entropy [closed]

What books introduce entropy in a intuitive, elementary way (at most, for a person with undergraduate physics studies)? The book should not necessarily introduce entropy in relation only to ...
0
votes
1answer
30 views

How to prove that Gibbs state remains a gibbs state after evolution?

Gibbs state is $$ \rho_G=\frac 1Z e^{-H/kT}=\sum_n \frac 1Z e^{-E_n/kT}|E_n⟩⟨E_n|. $$. In wikipedia, it is said that a Gibbs state is an equilibrium probability distribution which remains invariant ...
0
votes
1answer
44 views

If I prepare a state (density matrix) in Gibbs state, does it go to the lowest energy state at very low temperature?

Gibbs state is $$\rho_G=\frac{1}{Z} e^{-H/kT} = \sum_n \frac{1}{Z} e^{-E_n/kT}|E_n⟩⟨E_n| \, . $$ If $T$ goes to zero, does it mean the $\rho_G$ goes to the lowest energy state $|E_0⟩⟨E_0|$?
0
votes
0answers
48 views

Defining Thermodynamic beta in unit of second

If I define Thermodynamic beta in unit of second. Does this mean that: Boltzmann constant $k$ is unit-less? $T$ is in units of frequency (Hz) or Kelvin $K$? In this case, is defining Thermodynamic ...
2
votes
1answer
94 views

Two conflicting forms of equation of state of non-relativistic gas

I've run into two conflicting derivations of the equation of state of a non-relativistic gas. However, the derivations of the relativistic equation of state of both sources agree. I think maybe the ...
1
vote
0answers
48 views

Mixed Gas Absorbtion

Consider a gas misture that contains two type of atom, A and B. The gas is in equilibrium at temperature $T$. If on the surface of the gas container there are M sites that can absorb an atom gas, and ...
0
votes
1answer
34 views

Water evaporation rate: temperature vs humidity

I have a hot tub which I keep at 100 degrees F, and the water has "a lot" of dissolved salts in it. If I leave it open, will it evaporate faster when it is hot and humid outside, or when it is cold ...
0
votes
2answers
55 views

Canonical partition function and counting

That's a silly silly question, so my apologies, but in this moment I could not reach out! Let's have a system made of a particle reservoir $R$, and a subsystem $S$. The total particle number is $N$. ...
0
votes
0answers
57 views

Statistical Mechanics Textbook [duplicate]

Although I'll be taking a course on statistical mechanics next term, I'm looking to work through the details of statistical mechanics on my own in the summer. Which textbook would one recommended. I ...