2019/06/03 by Udo Seifert
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann constant #Boltzmann equation #Boltzmann's entropy formula #Canonical ensemble #Entropy (arrow of time) #Entropy rate #Isolated system #Joint quantum entropy #Mathematics #Maximum entropy probability distribution #Maximum entropy thermodynamics #Physics #Principle of maximum entropy #Statistical physics #Statistics #Thermal Radiation and Cooling Technologies #Thermodynamics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/j.physa.2019.121822
published as Physica A 552, 121822 (2020) · Dedicated to the memory of Christian Van den Broeck
arxiv created 2019/06/03 · openalex publication_date 2019/06/13 · arxiv updated 2020/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive part of the entropy change does not become negative. However, for any finite system and small driving, the mean entropy change can well be negative. We derive these results using as micro-canonical entropy a variant recently introduced by Swendsen and co-workers called "canonical". This canonical entropy is the one of a canonical ensemble with the corresponding mean energy. As we show by refining the micro-canonical Crooks relation, the same results hold true for the two more conventional choices of micro-canonical entropy given either by the area of a constant energy shell, the Boltzmann entropy, or the volume underneath it, the Gibbs volume entropy. These results are exemplified with quenched N-dimensional harmonic oscillators.