SciPost Submission Page
Comparative Microscopic Study of Entropies and their Production
by Philipp Strasberg, Joseph Schindler
Submission summary
| Authors (as registered SciPost users): | Philipp Strasberg |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2403.09403v1 (pdf) |
| Date submitted: | 2024-03-25 13:16 |
| Submitted by: | Strasberg, Philipp |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on Boltzmann, Gibbs or canonical entropy). This is done for the archetypal nonequilibrium setup of two systems exchanging energy, modeled here with random matrix theory, based on numerical integration of the Schroedinger equation. We consider three types of pure initial states (local energy eigenstates, decorrelated and entangled microcanonical states) and three classes of systems: (A) two normal systems, (B) a normal and a negative temperature system and (C) a normal and a negative heat capacity system. We find: (1) All types of initial states give rise to the same macroscopic dynamics. (2) Entanglement and diagonal entropy sensitively depend on the microstate, in contrast to all other entropies. (3) For class B and C, Gibbs-volume entropies can violate the second law and the associated temperature becomes meaningless. (4) For class C, Boltzmann-surface entropies can violate the second law and the associated temperature becomes meaningless. (5) Canonical entropy has a tendency to remain almost constant. (6) For a Haar random initial state, entanglement or diagonal entropy behave similar or identical to coarse-grained-observational entropy.
Current status:
Reports on this Submission
Report 1 by Francesco Buscemi on 2024-4-28 (Invited Report)
Strengths
1- The paper is very well written.
2- The strengths and weaknesses of the numerical analysis presented are honestly explained.
Weaknesses
1- I didn't find any particular weaknesses, other than those listed by the authors themselves, and I don't think they affect the results presented.
Report
I enjoyed reading this work: it's solid science and a useful, if not exactly thrilling, addition to the debate about micro and macro entropies. The message it wants to convey is clearly explained and ultimately delivered in a clear way, as expected. I am happy to recommend it for publication. (But see requested changes below.)
Requested changes
1- The story that von Neumann suggested the name "entropy" to Shannon with the infamous tongue-in-cheek comment seems to be a factoid rather than a fact; Shannon denied it ever happened. See https://www.eoht.info/page/Neumann-Shannon%20anecdote
2- I would find it very useful to have all the entropies and cases considered summarized in some sort of table.
3- I would also find it useful if the Authors made their code available for other people to inspect and use. I believe this is also required by this journal's policies (see point number 6 in the "General required acceptance criteria")
Recommendation
Ask for minor revision