Abstract
The observed general tune-asymmetric behavior of macroscopic systems—embodied in the second law of thermodynainics—arises naturally from time-symmetric microscopic laws due to the great disparity between macro and inicro-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-asynunetric equations accurately describe the observed behavior of 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.
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Lebowitz, J.L. (1995). Microscopic reversibility and macroscopic behavior: Physical explanatoins and mathematical derivations. In: Brey, J.J., Marro, J., Rubí, J.M., San Miguel, M. (eds) 25 Years of Non-Equilibrium Statistical Mechanics. Lecture Notes in Physics, vol 445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59158-3_31
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DOI: https://doi.org/10.1007/3-540-59158-3_31
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