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

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61 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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99 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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91 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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32 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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51 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 ...
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1answer
25 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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49 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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32 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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45 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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60 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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161 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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41 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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56 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 ...
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106 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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23 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
64 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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65 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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30 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 $E+\delta E$: ...
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140 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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42 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: ...
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84 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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16 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 - ...
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1answer
114 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: $$\frac{1}{N}\ln Z ~=~ \ln(2 \cosh^2(\beta J)) $$$$+ ...
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59 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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53 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 $t$ ...
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63 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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47 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 ...
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114 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: ...
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65 views

Different kinds of trace for statistical ensembles

In the chapter 7 of the book "A Modern Course in Statiscal Physics" by L. Reichl, we found $Tr[\hat{\rho}]=1$ for microcanonical ensembles and $Tr_N[\hat{\rho}]=1$ for canonical and grandcanonical ...
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104 views

Why is probability proportional to $ \ e^{-E/kT}$? [duplicate]

Why is the probability for say the Ising model to be found in state of energy E proportional to $e^{-E/kT}$ ? Is this some postulate or can it be derived from simpler principles?
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109 views

What are the fundamental “axioms” of statistical mechanics? [closed]

I have previously heard that some scientists are interested in trying to reformulate statistical mechanics in different ways to try and create new ways to solve novel problems. This got me wondering, ...
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29 views

Why is it inappropriate to calculate free energy change from end points alone?

In molecular dynamics, free energy changes are estimated using a variety of protocols to establish a path between the starting and ending states. The classic example is umbrella sampling in which a ...
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34 views

Brownian Ratchet Plausibility

Alright I'm going to throw whatever reputation I have on the line here. And yes this is a serious question. Apologies for the shoddy imagery. I had a couple ideas to get the Brownian Ratchet to ...
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3answers
212 views

How can I intuitively understand the Boltzmann factor?

It is known that for a system at thermal equilibrium described by the canonical ensemble, the probability of being in a state of energy $E$ at temperature $T$ is given by the Boltzmann distribution: ...
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74 views

Could the uncertainty principle theoretically be violated at 0 K? [duplicate]

Ok so please excuse me if the following mental argument is completely ridiculous or obviously flawed :P I was reading about how, even at 0 K (assuming we could experimentally reach such a ...
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32 views

Phase separation - density functional theory

I would like to get the equilibrium density profile $\rho(x)$ of a non ideal gas that has phase separated. I start by defining a simple free energy density. The total free energy $F[\rho]$ is a ...
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35 views

Molecular dynamics and detailed balance

In developing methods to perform Monte Carlo simulations one sufficient condition to preserve the stationarity of the target probability distribution is to impose detailed balance i.e. [Gardiner page ...
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5k views

Is there a thermodynamic limit on how efficiently you can solve a Rubik's cube?

Suppose I build a machine which will be given Rubik's cubes that have been scrambled to one of the $\sim 2^{65}$ possible positions of the cube, chosen uniformly at random. Is it possible for the ...
2
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1answer
141 views

Quantum ideal gas - Canonical ensemble - Occupation number summation notation (Huang)

(Question at the end, in bold, marked with an b)) For the quantum ideal gas, the hamiltonian (operator) of the system is: \begin{align} \mathcal H=\sum_{i=1}^N H_i=\sum_{i=1}^N \frac{P_i^2}{2m} ...
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46 views

Partition function for a two state system

We have a system of two energy states and we treat classical distinguishable and indistinguishable particles respectively. For the distinguishable case I thought that all in the left one one left ...
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1answer
45 views

Reversible and Quasi static processes

Do we have any proof that reversible processes are always quasi static or is it just a fact that hasn't been violated till date? If there is a proof then please provide a link.
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71 views

Sum over momentum states

In our lecture we used quite a couple of times that the sum over momentum states can be approximated by an integral over them. But instead of substituting $\sum_p \rightarrow \int d^3p$, we replaced ...
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21 views

Dimension of the Hilbert space of the restricted surface-on surface (RSOS) model

Right now I'm reading a paper on inversion identities for RSOS models, which you can find here. To give you a short introduction: The RSOS model is a face model, with a height variable assigned to ...
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1answer
63 views

Joule Thomson effect

I have difficulties to understand the Joule Thomson coefficient given on the wikipedia page. It says that $(\partial_p T) = \frac{V}{C_p}( T \alpha -1)$. Now my problem is that I don't know about ...
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1answer
40 views

Density depletion for Fermions

In my recent advanced statistical physics class, I read about the density depletion of Fermions, which are "defending" a given volume around them against other Fermions, while the exchange hole ...
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44 views

What is the argument for detailed balance in chemistry?

Detailed balance is an important property of many classes of physical systems. It can be written as $$ \frac{p_{i \to j}}{p_{j \to i}} = e^{\frac{\Delta G}{k_B T}},\tag{1} $$ where $i$ and $j$ ...
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248 views

Definition of stress at the microscale

Take, for simplicity, a Lennard-Jones fluid below the critical temperature, which is to say that there is a phase separation into fluid and gas and thus an interface is formed. The macroscale picture ...
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61 views

Why is the isothermal compressibility of the ideal boson gas larger than of the classical ideal gas?

Recently I came across (or well, derived in a lecture) the isothermal compressibility for an ideal boson gas. This was done in the context of statistical physics, using the quantum version of the ...
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301 views

Velocity Maxwell-Boltzmann distribution for dummies

I have a volume with N molecules; I need to assign to each particle a velocity vector: $$|\mathbf{v}_{i}|=[v_{x}, v_{y}, v_{z}]^{T}$$ for the i-th molecule; the velocities must fallow the ...
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1answer
30 views

Can a Fermi gas and a Bose gas be both at the same pressure and temperature?

The title says it all: can a Fermi gas and a Bose gas be both at the same pressure and temperature? It comes from a quiz about statistical mechanics