1996/05/29 by Joel L. Lebowitz, Lebowitz, Joel L.
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chemical Physics (physics.chem-ph) #Condensed Matter (cond-mat) #FOS: Physical sciences #Phase Equilibria and Thermodynamics #Theoretical and Computational Physics #chem-ph #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9605183
25 pages, 4 figures available upon request, in 25 Years of Non-Equilibrium Statistical Mechanics, Proceedings, Sitges Conference, Barcelona, Spain, 1994, in Lecture Notes in Physics, J.J. Brey, J. Marro, J.M. Rubi and M. San Miguel (eds.), Springer, 1995
arxiv created 1996/05/29 · openalex publication_date 1996/05/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More specific features of macroscopic evolution depend on the nature of the microscopic dynamics. In particular, short range interactions with good mixing properties lead, for simple systems, to the quantitative description of such evolutions by means of autonomous hydrodynamic equations, e.g., the diffusion equation. These deterministic time-asymmetric equations accurately describe the observed behavior of \it individual macro systems. Derivations using ensembles (or probability distributions) must therefore, to be relevant, hold for almost all members of the ensemble, i.e., occur with probability close to one. Equating observed irreversible macroscopic behavior with the time evolution of ensembles describing systems having only a few degrees of freedom, where no such typicality holds, is misguided and misleading.