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

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151 views

Bolzmann entropy [duplicate]

The Boltzmann entropy is defined as the logarithm of the phase space volume (E). Is there a reference, book, paper which shows where this definition comes and how it is equal to the phase space ...
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1answer
730 views

Probability of finding n particles in a volume v

I'm trying to calculate the probability of finding $n$ particles in a certain volume $v$ in a system with a total of $N$ particles and total volume of $V$. My problem is that I've tried two approaches ...
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3answers
694 views

Why the temperature is getting lower when the universe is expanding

As we know, if an ideal gas expands in vacuum, as its energy is unchanged, the temperature remains the same. An ideal gas's energy does not depend on volume. In general, the energy is $kT$ times the ...
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1answer
289 views

Scale invariance and self organized criticality

On wikipedia i have found this statement: In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems which have a critical point as an attractor. Their ...
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1answer
223 views

Equivalent system in Centre manifold theory

I was studying the centre manifold theory. It says (see Kuznetsov page 155, theorem 5.2) that the system on the left side of the picture is topologically equivalent to the one on the right. $ ...
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2answers
102 views

Susceptibilities and response functions

It is often confusing whether a susceptibility is the same as a response function, specially that often they are used interchangeably, in the context of statistical mechanics and thermodynamics. Very ...
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100 views

When the low temperture reservoir with negative temperture (Kelvin), such as Ising model, is the efficiency of ideal heat engine larger than 1?

The ideal Carnot engine works between two heat reservoir with two temperatures $t_h$ and $t_l$. Its efficiency is then $1-\frac{t_l}{t_h}$ . If the low temperture reservoir is the Ising model with ...
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2answers
972 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
597 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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1answer
134 views

Hamiltonian of a simple graph

I have a spin system: As shown in the picture, there are two spins S1 and S2, and a pair of interactions between them. One is a ferromagnetic interaction and the other is anti ferromagnetic ...
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1answer
41 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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37 views

Independent boson model with an arbitrary finite-dimensional impurity

The independent boson model consists of the following Hamiltonian: $$ H_s = E \sigma^z $$ $$ H_b = \sum_k \omega_k b^{\dagger}_kb_k $$ $$H_{sb} = \sigma^z \sum_k (g_k b_k + g_k^{\ast}b^{\dagger}_k).$$ ...
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76 views

Can one stimulate emission of a photon with an energy different from the emitted photon?

Suppose I have a three-level system with $E_0$ the ground level, $E_1$ the intermediate and $E_2$ the upper level. In thermal equilibrium they will have a certain probability distribution according to ...
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1answer
249 views

Math for Thermodynamics Basics

I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present. There is a section that i can not understand: ...
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2answers
550 views

Statistical interpretation of Entropy

I'm preparing my statistical physics course, and while writing the lecture notes it says that a system with non distinguishable particles has much less microstates asociated with a particular ...