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

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42 views

What does a correlation function measure and how does it do this mathematically?

I would really appreciate if someone could explain. What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ ...
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1answer
24 views

Why does this derivation of the dependence of free energy on pressure not work?

It is well known that the Gibbs Free Energy of a gas depends on the pressure via the following formula: $$G_m(p) = G^\circ_m + RT\ln{\frac{p}{p^{\circ}}}$$ Where $G_m$ is the molar gibbs free energy ...
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2answers
40 views

According to Liouville's theorem, why is the measure on an energy-surface different from the measure on the phase space in general

I recently read Khinchin's derivation of Liouville's theorem. I was able to follow the math for the most part, however I was hoping for an intuitive understanding about why the form of the measure on ...
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1answer
15 views

What is an expression/physical law that relates high frequency thermal fluctuations to gas pressure?

When a gas is compressed the 'ideal gas law' can predict what the increase in gas temperature will be. But that's just a mean temperature, right? At a quantum level the frequency of molecular ...
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1answer
19 views

Bose-Einstein phase transition and average number of part in state l

The explanation I have trouble understanding is this: The average number of particles $<n_l>$ on state $l$ is $$<n_l>=\frac{z}{e^{\beta \epsilon_l}-z}$$ where $z=e^{\beta \mu '}$ is the ...
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2answers
58 views

Why is most probable speed not equal to rms speed for an ideal gas?

The rms speed of ideal gas is $$\mathit{v_{rms}} = \sqrt{\dfrac{3RT}{M}}.$$ The most probable speed is the speed where $\dfrac{dP(\mathit {v})}{dv} =0$ where $P(\mathit{v})$ is the probability ...
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8 views

otto engine efficiency van der waals gas

I am trying to work out the efficiency of an Otto engine with the working substance being a Van der Waal's gas. I know that $ (P + Na^2 /V^2)(V-Nb)^α = const$ and that α= Cp/Cv. And then that $ ...
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14 views

Microstates and macrostates [closed]

What is relationship between microstate and Schrödinger wave equation and wave function How to vizualize the relationship
3
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2answers
59 views

Simplest example of spontaneous breaking of time reversal symmetry

Consider a two-dimensional fluid flow, confined to a square, where the bottom is held at a higher temperature than the top. With appropriate choices of the parameters, this will form a single ...
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1answer
28 views

Is there an equivalent probability distribution for fermions and bosons to the expression for distinguishable particles

So the particle distribution of two particles is simply $$ P_{12}=P_1(r_1)P_2(r_2) $$ where $ P_{12}$ is simply the modulus of the total wavefunction squared and $ P_1 $ and $ P_2$ are the the ...
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0answers
24 views

Number of states of a simple system

I am trying working on a problem in which there are two energy states $E_{1}<E_{2}$, and three different (i.e. distinguishable) particles. I cannot decide if the order of the particles matters. ...
2
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2answers
44 views

Temperature in statistical mechanics and differentiating entropy

In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of ...
4
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1answer
79 views

What exactly happens at the second-order phase transition of the 2D Toric code?

For a 2D Toric code specified by $$H = -J_s\sum_{s} \prod_{j\in s} \sigma^x_j - J_p\sum_{p} \prod_{j\in p} \sigma^z_p - h_x\sum_{l} \sigma^x_l - h_z\sum_{l} \sigma^z_l$$ where $s$ denotes stars, $p$ ...
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0answers
15 views

Difference between molecular dynamics and direct simulation Monte Carlo

I just started studying about rarefied gases and I came across the concepts of Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC); so here is my question: How are these two fields ...
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1answer
27 views

Show that, for two large systems in thermal contact, the number $\Omega^{0}(E^{0},E_1)$ can be expressed as a Gaussian in the variable $E_1$

This problem below is from the book "Statistical Mechanics" by Pathria. The author defined the number of microstates of a system with two subsystems exchanging energy as: $$\Omega_1(E_1) ...
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21 views

How to understand the Bose glass phase has infinite superfluid susceptibility?

The Bose glass phase is characterized by a gapless excitation spectrum, exponential decay of superfluid correlations, finite compressibility and infinite superfluid susceptibility. The disordered ...
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0answers
28 views

grand-canonical ensemble

I was wondering if the following reasoning is correct for example for electrons in the classical or qm grand-canonical ensemble? Is it always valid in the grandcanonical ensemble to calculate the ...
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0answers
31 views

How to apply Wick's theorem in 2nd quantization for Spin Density Operators?

I am trying to work out a correlation function consisting of two spin density operators. Once I rewrite everything in 2nd quantized form, I am unsure of how to apply wicks theorem because the paul ...
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1answer
71 views

Is information a form of energy? [closed]

To better describe my question, do the following experiment: Calculate x=12+26+67+71 Now you might have spent some time in getting the answer. You burnt sugar, you used up energy to get the ...
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2answers
109 views

Extensive variables in thermodynamics

Extensive variables in thermodynamics are those which scale linearly with the system size. It is known that a ratio of two extensive variables is an intensive variable. Now, the number of particles ...
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2answers
86 views

Definition of Fermion [closed]

Recently, I encounter a problem about the definition of Fermion operator. In our standard textbooks, the Fermions are defined by their exchange/braiding property, that is, if a minus sign appears by ...
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1answer
41 views

Thermodynamics vs Kinetics

As a chemical reaction approaches equilibrium, one of forward or backward reactions dominate the other. According to thermodynamics, this is because the gibbs free energy change for one is negative. ...
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1answer
41 views

Entropy and Gibbs Free Energy

I've been struggling with the notion of entropy and gibbs free energy for almost three days now. Different sources on and off the internet say different things about entropy. Gibbs Free Energy is ...
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0answers
68 views

Grand canonical Hamiltonian

How to explain introducing "grand canonical" Hamiltonian $$ \hat{H'}= \hat{H}-\mu \hat{N} $$ when we study a quantum system with fixed chemical potential? I understand such a substitution in a ...
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1answer
78 views

Does it make sense to define the mean free path in quantum mechanics?

The mean free path defined in classical molecule dynamics has a strong classical flavor. Is it sensible to generalize the idea to quantum mechanics?
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1answer
23 views

Fermi distribution and ideal gas

I was wondering about the following: If we have ideal gas particles, then $E \ge 0$, so one would expect that the state $E=0$ is occupied with probability one for low temperatures, but this is not ...
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0answers
42 views

Calculating the heat transfer into CO$_2$ gas at a constant pressure

I am having trouble with a homework question and I am just not sure how to attack it. We have not covered how to deal with non-ideal gases yet, and we are expected to answer this question without that ...
0
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1answer
18 views

Specific Heat of a Fermi Liquid

Let me give a bit of context before asking the actual questions: In the second edition of Condensed Matter Physics, Michael P. Marder derives the specific heat of Fermi liquids in chapter 17.5.4. He ...
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1answer
47 views

Adiabatic processes and the First Law

The first law of thermodynamics in my notes is : $\Delta E=\Delta Q +\Delta W $. Then later in my notes for an adiabatic process: $\Delta Q \implies dE=-pdV$. Then for a monatomic gas ...
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25 views

Books/resources for statistical field theory

I was wondering if anyone knows good, approachable textbook or other resources about statistical field theory (topics like in Kardar's Statistical physics of fields: lattice models, mean field theory, ...
0
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0answers
29 views

What are the Fermi and Debye temperature constants?

What are the Fermi temperature and Debye temperature constants? We were discussing these in class and I don't fully understand what these constants are or why we have them. Can anyone explain?
3
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1answer
34 views

Can you thermally pump a laser? (and problems with population inversion)

Recently a question was asked during a lecture about the possibility of thermally pumping a laser. The lecturer claimed that this is pretty impractical as typical transitions in the visible light ...
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134 views

Confusing Chemical potential of mixtures

I feel that there are very few textbook that treat the chemical potential of mixtures in an understandable clear way, which is why I wanted to ask here about certain things? Although I do not have a ...
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32 views

Is any phase associated with some fixed point in Renormalization Group?

In Wilson's paper I found a lot of discussion in expansions near a fixed point. He suggested that each fixed point is associated with a regime of the system. Like the fixed points of Anderson's Model, ...
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0answers
39 views

Ising Model with All Spins Interacting with All Other Spins

I am studying the Ising model with all spins interacting with all other spins and have formulated $Z$. I am trying to understand what it means to study at large N but not infinite N. I know that at ...
2
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1answer
100 views

How do sharp time intervals arise in a mesoscopic/macroscopic system?

$\newcommand{\ket}[1]{\left|#1 \right\rangle}$ $\newcommand{\bra}[1]{\left\langle #1 \right|}$ For a physical process in a mesoscopic/macroscopic system, how exactly can one deduce the time that ...
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0answers
21 views

Can a gas be modelled as a low density blackbody, if we want to consider how detectable it will be in space?

The answer to this question taught me about the sort of parameters I need to consider if I want to consider how "detectable" an object in space is. I want to consider the detectability of a ...
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2answers
53 views

Proof of the Boltzmann factor

The following derivation of the Boltzmann factor is obviously wrong, or incomplete: $$p(E) \propto \Omega(U-E)$$ Consider the Taylor expansion of $\ln\Omega(x)$: $$\ln\Omega(U-E)\approx \ln ...
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0answers
48 views

Resource recommendation: book that does not cover statistical mechanics specifically with thermodynamics in mind?

Statistical mechanics by its plain definition is a broad field, but most introductory textbooks focus on its applications in thermodynamics. Are there introductory texts that take up a broader view of ...
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1answer
19 views

Volume of highdimensional Sphere vs volume of spheres shell

When calculating the phase space volume $\Omega$ in the microcanoncial ensemble with fixed energy $E$, one integrates over a shell that includes all energies in between $E$ and $E+\delta E$: ...
5
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1answer
128 views

How hot is your photon?

This question comes from my answer to the question Can a cubic meter of space at absolute zero have any object with mass inside? and the related discussion under it. To summarize, I stated that the ...
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0answers
36 views

Entropy Inequalities

Hey I am reading this paper Entropy Inequalities by Araki and Lieb. I am trying to prove the following lemma: $$S^1+S^2\leq S^{12}+S^{23}$$ using the following lemmas: ...
4
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1answer
58 views

Deriving Boltzmann statistics from the maximum entropy principle

In some lecture notes I have, the author derives the expectation value of the occupation numbers for a discrete system of fermions as follows: Consider all states that have a certain energy ...
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0answers
15 views

Probabilistic interpretation of Hausdroff measure [closed]

My problem is to find/derive a pdf in terms of a parameter which closely resembles Hausdroff measure and the idea stems from the following concepts. Please correct me where I go wrong. Paper1 - ...
1
vote
1answer
93 views

Expansion of Onsager's Exact Partition Function for 2D Ising Model

We have a question where we are given the exact expression for the 2D Ising model partition function: $$\frac{1}{N}\ln Z ~=~ \ln(2 \cosh^2(\beta J)) $$$$+ ...
1
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0answers
41 views

Statistical mechanics vs. many-body theory

Where is the basic difference of statistical mechanics with many-body physics? What are the systems which cannot be studied in statistical mechanics but in many body theory? After all we know ...
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1answer
37 views

Estimate the persistence length of a rubber band [closed]

Not much more to say here, it's all in the question. The best, most convincing estimate will be chosen as the correct answer. EDIT: Assume the rubber band is at room temperature, with thickness $t$ ...
0
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1answer
52 views

In what ways is Tolman's book on statistical mechanics out-of-date?

I am considering purchasing Tolman's The Principles of Statistical Mehcanics (not to be confused with his Statistical Mechanics with Applications to Physics and Chemistry), but I was wondering if, and ...
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0answers
41 views

How can energy be partitioned equally when energy is relative?

According to the Equipartition theorem in a system at equilibrium the energy should be on average be divided equally between the available degrees of freedom. The most common examples are the three ...
3
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47 views

Two-point correlation function for Potts Model

Consider the Potts model with three states , $\sigma (x) \in \{ 1, e^{2 \pi i/3}, e^{4 \pi i/3} \}$. I wanted to make sure that the following definition for two-point correlation function is correct: ...