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

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13answers
9k 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 ...
0
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1answer
198 views

Meaning of Strongly and Weakly Degenrate

In ideal Bose and Fermi gases we often use Either Strongly Degenerate Ideal Bose/Fermi or Weakly Degenerate Ideal Bose/Fermi gas. As far as I know mathematically if the fugacity $z=e^{\beta\mu}$ close ...
1
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0answers
24 views

Collision term in Boltzmann Equation

In Dodelson's Book, chapter 3, we have the collision term in Boltzmann equation is written as $$\int\frac{d^3p_1}{(2\pi)^32E_1}\int\frac{d^3p_2}{(2\pi)^32E_2}\int\frac{d^3p_3}{(2\pi)^32E_3}\int\frac{...
5
votes
1answer
45 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
votes
4answers
27 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
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1answer
24 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^{\...
13
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6answers
7k views

Why was the universe in an extraordinarily low-entropy state right after the big bang?

Let me start by saying that I have no scientific background whatsoever. I am very interested in science though and I'm currently enjoying Brian Greene's The Fabric of the Cosmos. I'm at chapter 7 and ...
5
votes
2answers
213 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 ...
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{...
4
votes
1answer
213 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
0
votes
1answer
257 views

Chemical Potential as a function of Temperature

I have considered an ideal fermi gas. Then, we can obtain an expression for chemical potential as a function of Temperature. I want to understand the physical significance to it or what it really ...
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
votes
1answer
71 views

Physicists use of “Information” [closed]

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 ...
4
votes
1answer
202 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 ...
3
votes
0answers
65 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 ...
2
votes
1answer
155 views

Periodic ground state 1-dim ising model

Good evening! I'm at the beginning of my study about the Ising model and it has been proposed to me this problem: Find all periodic ground-state configuration for the following one-dimensional Ising ...
0
votes
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. ...
0
votes
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 ...
2
votes
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
27
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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 ...
0
votes
1answer
133 views

Thermal average, thermal fluctuations

I've a doubt concerning the physical meaning of "thermal average" and the "thermal fluctuation" in the canonical ensemble. Let's consider a very simple thermodynamic system: N particles, at fixed ...
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
14 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 ...
5
votes
2answers
189 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf j_{\...
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: $...
5
votes
1answer
779 views

Pauli paramagnetism for electrons with external magnetic field

Apparently it is to be shown that for electrons under an external magnetic field, in the limit as $B\to 0 $ $$ \chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)} $$ ...
1
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1answer
54 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 ...
8
votes
2answers
256 views

Itô or Stratonovich calculus: which one is more relevant from the point of view of physics?

Langevin equation provides an example of a physical model which involves a differential equation with a stochastic term. Now, I wonder, how should one treat this? When I studied stochastic processes, ...
1
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2answers
343 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 ...
2
votes
2answers
93 views

Can an Ergodic dynamical system approach equilibrium?

An ergodic dynamical system $(\Omega,\phi^t,\mu)$ is such that the time average $\bar{f}$ of every function $f\in L_1(\Omega,\mu)$ equal the space average $\langle f \rangle_\mu$, i.e. the system ...
1
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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 ...
30
votes
3answers
27k views

First and second order phase transitions

Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article starts by explaining that Ehrenfest's original definition was that a first-order ...
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 ...
21
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5answers
7k views

Is there any proof for the 2nd law of thermodynamics?

Are there any analytical proofs for the 2nd law of thermodynamics? Or is it based entirely on empirical evidence?
10
votes
1answer
341 views

2d Ising model in CFT and statistical mechanics

When I recently started to read about conformal field theory, one of the basic examples there is the so called Ising model. It is characterized by certain specific collection of fields on the plane ...
4
votes
2answers
758 views

About Boltzmann H-theorem

What is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize ...
25
votes
4answers
2k views

The unreasonable effectiveness of the partition function

In a first course on statistical mechanics the partition function is normally introduced as the normalisation for the probability of a particle being in a particular energy level. $$p_j=\frac{1}{Z}\...
0
votes
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 ...
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 ...
3
votes
1answer
198 views

Entropy of the cosmological constant and the laws of thermodynamics?

Convention The convention being used is: $ A_{C} = $ The classical variable Premise Consider the following toy-model universe: A universe with a positive cosmological constant. Basic ...
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 ...
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 ...
2
votes
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 ...
0
votes
1answer
224 views

What is the physical fundamentals of Pascal's law

Pascal's law or the principle of transmission of fluid-pressure (also Pascal's Principle) is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible ...
3
votes
1answer
409 views

Scale invariance and self organized criticality

On wikipedia I have found this statement: In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems which have a critical point as an attractor. Their ...
4
votes
1answer
240 views

Scale invariance in sandpile model and forest fire model

I asked a similar question but the wrong way here. Because my intention was to ask about non thermodynamic system, I will be more specific: What is the relation between critical behaviour and the ...
25
votes
4answers
3k views

How do you prove $S=-\sum p\ln p$?

How does one prove the formula for entropy $S=-\sum p\ln p$? Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law ...
18
votes
6answers
2k views

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? I have never seen dissipation explained, although what I have seen a lot is descriptions of ...
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 ...