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

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How can I explicit the energy dependence of the Maxwell-Boltzmann distribution?

I'm having a bit of a problem figuring out the energy dependent Maxwell-Boltzmann distribution. According to my book (Ashcroft & Mermin) they write the velocity dependent distribution as: ...
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Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
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354 views

Is there really such a thing as an irreversible process?

If an isolated system goes from a state A to B, will it always eventually fluctuate back to state A? If not, give an simple example. Is it right to say that entropy only says that the probability ...
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Discussions of the axioms of AQFT

The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, ...
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What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble?

In the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$: $$ \langle \hat n_r\rangle^{\pm} \ \propto \ ...
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313 views

Any open areas to work in non equilibrium thermodynamics for a Phd student? [closed]

I see that many papers written on fundamentals of thermodynamics(theory) nowadays are by some old professors somewhere(there may be exceptions). Most active young faculty don't seem to be seriously ...
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771 views

Spontaneous conversion of heat into work at negative temperatures

Consider a heavy macroscopic object moving in a gas. Friction causes its kinetic energy to be converted into heat. Thermodynamically, there is (effectively) no entropy associated with the kinetic ...
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188 views

Why is chemical potential, μ=0 when calculating critical temperature of BECs?

How do we justify taking the chemical potential, $\mu$ as $0$ when calculating the critical temperature of Bose-Einstein Condensates (BECs)? I apologise as I do not how to use LaTeX, for if I did the ...
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249 views

Why are the eigenvalues of a linearized RG transformation real?

The RG transformation $R_\ell$ maps a set of coupling constants $[K]$ of a model Hamiltonian to a new set of coupling constants $[K']=R_\ell[K]$ of a coarse-grained model where the length scale is ...
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4k views

What are the six degrees of freedom of the atoms in a solid?

A monoatomic ideal gas has heat capacity $C_v=1.5$ which comes from the three translational degrees of freedom. For solids at high temperature, $C_v=3$, implying six degrees of freedom. What are ...
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371 views

Renyi entropy in physical systems

We know that the Shannon entropy $H(P)=- k_{\mathrm{B}}\sum_i p_i \ln p_i$ is mostly the entropy of the thermodynamic systems. Does the Renyi measure $H_{\alpha}(P)=\frac{1}{1-\alpha}\log \sum ...
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392 views

What is the information geometry of 1D Ising model for a complex magnetic field?

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
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82 views

Understanding Gibbs $H$-theorem: where does Jaynes' “blurring” argument come from?

According to this Wikipedia article, the $H$-theorem was Boltzmann's attempt to demonstrate the irreversible increase in entropy in a closed system starting from reversible microscopic mechanics. ...
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1answer
874 views

Why is it difficult to mix helium and nitrogen gases?

I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for ...
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2answers
353 views

Why does bad smell follow people (assuming they are not the source)?

When you are sitting in a room where there is a source of bad smell, such as somebody smoking or some other source of bad smell, it is often a solution to simply move to another spot where bad smell ...
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1answer
112 views

Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...
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5answers
10k views

What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
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1answer
139 views

What it means to integrate over $n$ variables out of $N$, where $N>n$?

I was reading Theory of Simple Liquids, when I came across BBGKY hierarchy. In deriving the expression for the hierarchy, they integrate an integration of N variables over N-n variables to make the ...
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2answers
595 views

Physical significance of negative temperature

I read some answers regarding negative temperatures but I think my question is new. I want to know that what is the physical significance of negative temperature. Suppose I say a body has ...
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3answers
1k views

Does entropy really always increase (or stay the same)? [duplicate]

Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order. While unlikely, ...
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1answer
671 views

Why the chemical potential of massless boson is zero? [duplicate]

In Bose-Einstein condensation, the chemical potential is less than the ground state energy of the system($\mu<\epsilon_g$). But why does the massless boson such as photon have zero chemichal ...
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3answers
145 views

Does the second law of thermodynamics take into consideration of attractive interactions between particles?

If one searches Google or textbooks on 2nd Law of Thermodnamics, one usually finds a statement that is either equivalent or implies the following. The entropy of the universe always increases. But ...
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1answer
267 views

Maxwell-Boltzmann distribution for transport equations

I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use. As far as I know it should not be the MB distribution for ...
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1answer
2k views

Significance of the the Lagrange multipliers in statistical mechanics

In classic thermodynamics one can derive the Maxwell Boltzmann statistics by solving a Lagrange multipliers equation. In this process a new parameter $\beta$ is introduced to take account of the total ...
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3answers
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Definition of Fluctuations and Perturbations

The terms fluctuations and perturbations are frequently used in physics with different meanings. But they are confusing. Both terms seems to be same. Is there any one who can explain lucidly these ...
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Calculating quantum partition functions

...By quantizing we the get the following Hamiltonian operator $$\hat{H}=\sum_{\mathbf{k}}\hbar \omega(\mathbf{k})\left(\hat{n}(\mathbf{k})+\frac{1}{2} \right)$$ where ...
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1answer
149 views

Meaning of the symmetrisation postulate in absence of a proper model

My question is on the use of the concept of indistinguishable particles (in quantum mechanics) in a very general context and in particular in statistical mechanics. I have made clear some of my ...
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2answers
1k views

Must a reversible engine be a carnot engine?

I have this homework question: "Show that any reversible engine operating between T1 and T2 is a carnot engine." I think I have a solution, but it feels very hand-wavy. We know that any process that ...
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1answer
823 views

Ensemble of harmonic oscillators

I have some problems with problem 2.3 from Reif's Fundamentals of statistical and thermal physics: Consider an ensemble of classical one-dimensional harmonic oscillators. a) If we assume ...
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1answer
200 views

Uncertainty and Thermodynamics

Dilemma The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that $\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
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2answers
257 views

Reconstruction of information stored in an evaporating black hole from the emission spectrum?

For simple setups, where the radiation field deviates not too far from thermodynamic equilibrium (< 10 %), corrections to the Planckian thermal emission spectrum can be calculated (and measured) ...
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486 views

Irreversible expansion and time reversal symmetry

Suppose there are N non-interacting classical particles in a box, so their state can be described by the $\{\mathbf{x}_i(t), \mathbf{p}_i(t) \}$. If the particles are initially at the left of the box, ...
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Counting classical microstates

In my notes it states that the convention for summing over the classical states is $$\sum_{\Gamma} \longrightarrow \frac{1}{N!}\int \prod_{i=1}^N \frac{d^3q_id^3p_i}{h_0^3} \tag1$$ Now I know that ...
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71 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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1answer
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Dr. Pierre-Marie Robitaille: On the Validity of Kirchhoff's Law

Lately I've been researching about the black-body spectrum and the historical development of Planck's Law. I mainly wanted to understand a little bit more why many different objects (Stars, Hot ...
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2answers
144 views

Do gravitational waves have entropy?

We know, according the current understanding of black holes and General Relativity, as well as quantum fields in General Relativity, that black holes have an entropy proportional to the area of the ...
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1answer
179 views

Canonical averages in a Fermi gas aka generalized Fermi-Dirac distribution

I am in the process of applying Beenakker's tunneling master equation theory of quantum dots (with some generalizations) to some problems of non-adiabatic charge pumping. As a part of this work I ...
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616 views

Applying the Maxwell–Boltzmann statistics to astrophysical objects

Quoting Wikipedia: In statistical mechanics, Maxwell–Boltzmann statistics describes the statistical distribution of material particles over various energy states in thermal equilibrium, when the ...
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3answers
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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 ...
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334 views

Mathematical probabilistic interepretation of probability amplitude

As a warning, I come from an "applied math" background with next to no knowledge of physics. That said, here's my question: I'm looking at the possibility of using probability amplitude functions to ...
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5answers
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Second law of Thermodynamics: Why is it only “almost” always true that entropy is non-decreasing? [duplicate]

Wikipedia - Second law of thermodynamics: ...the entropy of any closed system not in thermal equilibrium almost always increases. I understand that the second law of thermodynamics is based on ...
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3answers
423 views

Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution

Maxwell derived the shape of the probability distribution of velocity of gas particles by starting with just two assumptions. These are: The probability distribution is rotation invariant. The ...
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1answer
859 views

Intuition behind classical virial theorem

I am continuing to brush up my statistical physics. I just want to gain a better understanding. I have gone through the derivation of the classical virial theorem once more. I have thought about it, ...
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2answers
1k views

The analogy between temperature and imaginary time

There are many statements about the relation between time and temperature in statistical physics and quantum field theory, the basic idea is to interpret (inverse) temperature in statistics as "time" ...
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477 views

Continuous phase transition only hold for infinite systems. Real systems are finite, hence, a paradox

Second-order or continuous transitions are usually identified with non-analyticies within the free energy (which is proportional to the logarithm of the sum of exponentials). Such singularities are ...
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1answer
1k views

quantum mechanics current operators

How to derive the charge current and the energy current operators in second quantized form in Quantum mechanics ? Also if you could comment in a similar way on the entropy current operator, that will ...
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4answers
540 views

Why can $\beta$ not be linearly proportional to $T$, that is $\beta = constant \times T$?

$\beta$ in statistical mechanics is equal to $\frac{1}{k_BT}$ in in thermodynamics, but I do not understand why $\beta\propto T^{-1}$ instead of, say, $\beta\propto T$?
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Calculating the heat capacity of a system

I have started reading Statistical Physics by F. Mandl and I would appreciate some help with the following exercise A system consists of $N$ weakly interacting subsystems. Each subsystem possesses ...
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95 views

Probablistic interpretation of entropy

After taking a statistical mechanics course, I'm somewhat surprised that my intuitive highschool understanding of entropy doesn't match my current understanding. When I was introduced to entropy, I ...
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1answer
150 views

Evaluating low-temperature dependence of the BCS gap function

How does one go about evaluating the behavior of the BCS gap $ \Delta = \Delta(T) $ for $ T \to 0^+ $ under the weak coupling approximation $ \Delta/\hbar\omega_D \ll 1 $? In Fetter & Walecka, ...