All Questions
Tagged with quantum-statistics entropy
11 questions
6
votes
2
answers
334
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What is the number of quantum states compatible with isolated ideal gas macrostate $N,V,U$ and molecular mass $m$?
What is the degeneracy of an energy level $U$ of an ideal gas of $N$ particles with molecular mass $m$ in a volume $V$?
This sounds like a standard textbook problem about the Boltzmann entropy of ...
- 41.2k
5
votes
0
answers
112
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Questioning a calculation in Kapusta / Infinite entropy of a Fermi gas?
I am going through Kapusta's calculation of the free energy of a Fermi gas, and I find one of his steps dubious (and if I'm right, it would mean the free energy of a Fermi gas is either infinite or ...
- 3,557
0
votes
2
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71
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Why are $U$ and $V$ (and not $N$) the only extensive parameters for blackbody radiation?
In Chapter 3.6 of Callen, he remarks that the particle number $N$ does not appear in the thermodynamic description of blackbody radiation. Why is this? That is, in most simple systems of one component,...
- 1,261
1
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0
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117
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Different Definitions for "Gibbs' Entropy"
This question suggests that for the microcanonical ensemble, additional to the "usual" definition of entropy
\begin{align}
\omega(E)=Tr \delta(E-H) \\
S_B=\ln \omega(E)
\end{align}
(Called ...
- 6,955
0
votes
0
answers
44
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Entropy in Quantumstatistcs and Seckur-Tetrode-Equation
In my lecture we considerd a microcanonical ensemble with $E-\Delta \leq E_{\{n\}} \leq E$ with $E_{\{n\}}$ being the energy-eigenvalues of the Hamiltonian and $\{n\}$ being the quantum numbers. We ...
- 522
0
votes
0
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457
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Obtaining the number of quanta for a system of harmonic oscillators
So I need to find the entropy of a system made up of two harmonic oscillators having natural frequency $\omega_0$ and $2\omega_0$. The system is said to have a total energy of $E=(n+\frac12)\hbar\...
- 422
1
vote
0
answers
130
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Matrix formulation of maximum entropy
In E.T Jaynes' book "Probability theory: the logic of science" the maximum entropy principle is discussed as the way to choose out of all possible hypotheses agreeing with constraints, the ones that ...
- 1,277
2
votes
1
answer
448
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Fluctuations of free energy in quantum statistical mechanics
I want to calculate the fluctuation of the mean value of the free energy, $\langle F \rangle$, which I denote as $(\Delta F)^2 = \langle F^2\rangle - \langle F\rangle^2$. Since I have calculated the ...
- 1,403
2
votes
2
answers
1k
views
Can entropy be intensive?
Entropy typically is an extensive thermodynamic variable. Thus, if I combine two subsystems 1 and 2, the total entropy $S_{total} = S_1 + S_2$. This follows directly from the Boltzmann-entropy when we ...
4
votes
2
answers
3k
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Quantum entropy in term of density matrix
Why in von Neumann expression of quantum entropy we have trace of density matrix expression? Why don't off diagonal term play a role?
- 1,135
20
votes
2
answers
3k
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Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?
Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
- 58.3k