Microscopic Reversibility and Macroscopic Behavior: Physical Explanations and Mathematical Derivations

摘要

The observed general time-asymmetric behavior of macroscopic systems --embodied in the second law of thermodynamics -- arises naturally fromtime-symmetric microscopic laws due to the great disparity between macro andmicro-scales. More specific features of macroscopic evolution depend on thenature of the microscopic dynamics. In particular, short range interactionswith good mixing properties lead, for simple systems, to the quantitativedescription of such evolutions by means of autonomous hydrodynamic equations,e.g., the diffusion equation. These deterministic time-asymmetric equations accurately describe theobserved behavior of {\it individual} macro systems. Derivations usingensembles (or probability distributions) must therefore, to be relevant, holdfor almost all members of the ensemble, i.e., occur with probability close toone. Equating observed irreversible macroscopic behavior with the timeevolution of ensembles describing systems having only a few degrees of freedom,where no such typicality holds, is misguided and misleading.