Comparative microscopic study of entropies and their production
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 arc...
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2024-11-01
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| Online Access: | https://scipost.org/SciPostPhys.17.5.143 |
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| author | Philipp Strasberg, Joseph Schindler |
| author_facet | Philipp Strasberg, Joseph Schindler |
| author_sort | Philipp Strasberg, Joseph Schindler |
| collection | DOAJ |
| description | 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 Schrödinger 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. |
| format | Article |
| id | doaj-art-0c09a0155a774a9a93cd62e441b8ba28 |
| institution | OA Journals |
| issn | 2542-4653 |
| language | English |
| publishDate | 2024-11-01 |
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| spelling | doaj-art-0c09a0155a774a9a93cd62e441b8ba282025-08-20T02:23:45ZengSciPostSciPost Physics2542-46532024-11-0117514310.21468/SciPostPhys.17.5.143Comparative microscopic study of entropies and their productionPhilipp Strasberg, Joseph SchindlerWe 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 Schrödinger 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.https://scipost.org/SciPostPhys.17.5.143 |
| spellingShingle | Philipp Strasberg, Joseph Schindler Comparative microscopic study of entropies and their production SciPost Physics |
| title | Comparative microscopic study of entropies and their production |
| title_full | Comparative microscopic study of entropies and their production |
| title_fullStr | Comparative microscopic study of entropies and their production |
| title_full_unstemmed | Comparative microscopic study of entropies and their production |
| title_short | Comparative microscopic study of entropies and their production |
| title_sort | comparative microscopic study of entropies and their production |
| url | https://scipost.org/SciPostPhys.17.5.143 |
| work_keys_str_mv | AT philippstrasbergjosephschindler comparativemicroscopicstudyofentropiesandtheirproduction |