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

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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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3answers
270 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
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88 views

Simple estimation of the critical temperature of water

I'm trying to develop fermi estimation skills and I came up with a question for which I don't even know where to start from. Here goes: Is it possible to estimate the critical temperature (say in ...
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1answer
18 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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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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2answers
56 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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2answers
122 views

How does the second law of thermodynamics follow from low entropy of early universe?

One of the explanations of the second law of thermodynamics is that it goes back to the low entropy in the early universe (How do you prove the second law of thermodynamics from statistical ...
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7answers
888 views

Entropy increase vs Conservation of information (QM)

Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of ...
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1answer
80 views

How to prove the Bose enhancement factor $(1+f)$ and the Pauli blocking factor $(1-f)$ in Boltzmann equation?

For the collision integral in the Boltzmann equation for particles obeying different statistic, the factor is 1 for classical particles , 1-f for fermions, 1+f for Boson. While why it's exactly this ...
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2answers
49 views

Simplest example of spontaneous breaking of time 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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14 views

Microstates and macrostates [on hold]

What is relationship between microstate and Schrödinger wave equation and wave function How to vizualize the relationship
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2answers
40 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 ...
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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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2answers
295 views

Moving between degenerate vacua?

In spontaneous symmetry breaking, moving round the circular valley of Mexican hat potential doesn’t cost energy. These angular excitations are called Goldstone bosons. But doesn't the angular ...
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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. ...
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1answer
75 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, $p$ ...
18
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1answer
194 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each ...
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1answer
112 views

Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
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1answer
82 views

Ising model on lattices with (vertical side length) $\neq$ (horizontal side length)

Consider the Ising model with nearest neighbours interactions on a rectangular lattice $L\times M$. If $L=M$ (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit ...
3
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1answer
142 views

H-theorem and Boltzmann equation applied to Boltzmann distribution

Using the Boltzmann equation: $$ \frac{dH}{dt} = \int_0^{\infty} dr \int_0^{\infty} ds W(r,s)[p_r - p_s][\ln{p_r} - \ln{p_s}],$$ and assuming $p_r = e^{-\beta r}$, the equation looks like $$ ...
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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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4answers
194 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 ...
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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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1answer
26 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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4answers
389 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 ...
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2answers
103 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 ...
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20 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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1answer
69 views

Spontaneity / Free Energy of Non-Isothermal Process

I'm trying to determine a lower bound for the work input necessary to make an entropy-reducing process "spontaneous" in the sense that the 2nd law is not violated. For a constant temperature and ...
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1answer
209 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 ...
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1answer
542 views

How is the distribution probability in the canonical ensemble derived?

I'm confused by the derivation of the canonical ensemble, namely the origin of the probability density, that is the Boltzmann factor. Here's what I have: We have a system of particles with ...
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0answers
27 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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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. ...
6
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3answers
541 views

Analogue of Princeton Companion to Mathematics for Physics?

I would like to know if there are compendiums much like the Princeton Companion to Mathematics for physics (especially classical physics: fluid mechanics, elasticity theory, Hamiltonian formalism of ...
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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
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
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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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 ...
6
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3answers
1k views

Is there a phase transition between a gas and plasma?

Does a phase transition occur as a gas is heated to create a plasma? If so, is this a first or second order phase transition? Also, does the presence of a phase transition depend on the pressure or ...
6
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2answers
172 views

Why do phase transitions even exist? Why not smooth density change curves?

Why do phase transitions even exist? Why not smooth density change curves? What properties of matter, quantum or otherwise, predicts that matter will undergo phases at different pressures and ...
0
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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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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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0answers
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 ...
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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24 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, ...
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0answers
28 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?
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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 ...