1999/11/12 by Shin-ichi Sasa, S.-i. Sasa, Teruhisa S. Komatsu +1
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Control and Stability of Dynamical Systems #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1143/ptp.103.1
LaTeX 43 pages (using ptptex macros) with 11 figures
arxiv created 1999/11/12 · openalex publication_date 2000/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper discusses the thermodynamic irreversibility realized in high-dimensional Hamiltonian systems with a time-dependent parameter. A new quantity, the irreversible information loss, is defined from the Lyapunov analysis so as to characterize the thermodynamic irreversibility. It is proved that this new quantity satisfies an inequality associated with the second law of thermodynamics. Based on the assumption that these systems possess the mixing property and certain large deviation properties in the thermodynamic limit, it is argued reasonably that the most probable value of the irreversible information loss is equal to the change of the Boltzmann entropy in statistical mechanics, and that it is always a non-negative value. The consistency of our argument is confirmed by numerical experiments with the aid of the definition of a quantity we refer to as the excess information loss.