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

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Reference about probability to study statistical mechanics

I've started studying statistical mechanics but I feel that I need to understand probability better. There are tons of books on probabilities out there, but some of them just talk too much, with tons ...
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38 views

Number of particles in a box at thermal equalibrium

Consider a cube box of volume $V$ in thermal equilibrium at temperature $T$. We have 3 pieces of information: The probability of finding a particle of mass $m$ in the box having momentum in ...
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212 views

What happens in a gas of magnets?

This SMBC comic asks what happens if you make a gas of magnetic particles: I was wondering whether anyone has run into actual examples of this or something like it. A classical example similar to ...
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49 views

Landau's derivation of the law of entropy increase - clarification

In Landau&Lifshitz V: Statistical Physics the following derivation of the law of increase of entropy is given. I need help understanding several crucial steps; I'll briefly summarize the notations ...
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2answers
59 views

What is the theoretical instantaneous temperature of a gas?

When we measure the temperature of a gas we typically integrate the molecular collisions and wind up with an 'average' temperature due to the sensor comprising a relatively large thermal mass. And ...
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1answer
77 views

Partition function: Number of states? Doesn't add up for ising

While trying to really understanding the partition function in statistical mechanics, I tried looking at it for a 2D ising model, as that's been helpful for me for all kinds of thermodynamic values. ...
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50 views

Definition of quantum microcanonical ensemble in Landau&Lifshitz

I'm reading the first chapters of Landau&Lifshitz 's [Statistical Physics][1] and I don't understand the definition of the quantum microcanonical ensemble. The microcanonical distribution for a ...
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1answer
36 views

What is quantum states of a gas? Is it the principle quantum no.?

When we write that the possible quantum states of a system are $S=1,2,3.\dots$, how is that related with the four quantum numbers, especially with the spin of a particle? Also according to BE ...
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44 views

Chemical reaction A+B$\leftrightarrow$C. Equilibrium VS Non Equilibrium

Could you please confirm or say why I am wrong? Let us consider the steady state of the chemical reaction $A+B \leftrightarrow^{k_+}_{k_-} C$, with $k_+$ and $k_-$ the forward and backward rates. ...
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156 views

Number $g(T)$ of relativistic degrees of freedom as a function of temperature $T$

Let us consider the total number of relativistic degrees of freedom $g(T)$ for particle species in our universe: $$g(T)=\left(\sum_Bg_B\right)+\frac{7}{8}\left(\sum_Fg_F\right)$$ Where the sums are ...
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49 views

What is the use of Schwinger-Keldysh formalism?

In non-equilibrium statistical mechanics, there is this formidable formalism, called the Schwinger-Keldysh formalism. I have read about it, and I understand what it is. However, what I what to know ...
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31 views

Time evolution of the density of phase points for an ensemble

I want to calculate the time evolution of the density of phase points for an ensemble of N harmonic oscillators. However, I intended to do so without using the Liouville equation. Sure, I want to ...
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52 views

Is Boltzmann constant $k_B$ constant?

I heard in a lecture that Boltzmann constant $k_B$ is not constant in some special cases. Do you know the title of the article which contains this one? Do you think this idea is true?
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32 views

Debye-Huekel Theory and the continuum approximation

This question stems from a problem I was doing on the Debye-Hueckel theory. It says that the continuum approximation which underlies the Debye-Hueckel theory is valid provided that $\lambda_D \gg ...
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1answer
58 views

Why is the number of phonon modes in a solid restricted to a finite value?

Kittel's Thermal Physics (Amazon link) makes the statement: There is no limit to the number of possible electromagnetic modes in a cavity, but the number of elastic modes in a finite solid is ...
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46 views

Corrections to the Equipartitio theorem

Does anyone know why sometimes $E = \frac{3}{2}k_{b}T $ is written as $E = \pi k_{b}T$. Where does this come from?
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61 views

Understanding summations over microstates of a given function

I am struggling to understand how to sum over microstates in statistical mechanics. Consider an $N$-spin system where $N \gg 1$ and $\Gamma=\{n_i \}$ for $1 \leq i \leq N$ and each $n_i$ is equal ...
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42 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 ...
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114 views

Does a vacuum, suddenly opened, become hotter than its surroundings?

Suppose you have an insulated container that is equipped with a valve to let air in. Initially the container is evacuated. You then quickly open the valve, allowing air to rush in. What is the ...
3
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120 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
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48 views

2 level atomic system interacting with Black body radiation. Relaxation time issue

I am studying the transient regime of a 2 level atomic system ($N_1,N_2$) interacting with a blackbody radiation from a source at constant temperature $T_{nr}$. The initial state of the atomic system ...
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1answer
102 views

Calculating the entropy of a monatomic ideal gas

I am looking at the start of the consider how to calculate the entropy of a monatomic ideal gas. We need to determine the number of microstates in $E \leq \mathcal{H}(\Gamma) \leq E+\Delta$. The ...
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132 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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43 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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72 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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21 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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23 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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170 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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88 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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45 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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36 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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76 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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117 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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53 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
43 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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42 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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45 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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48 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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244 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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1answer
43 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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95 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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113 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
99 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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36 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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53 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 ...
2
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1answer
35 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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53 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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36 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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50 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
68 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 ...