 96163 Joel L. Lebowitz
 Microscopic Reversibility and Macroscopic Behavior: Physical
Explanations and Mathematical Derivations
(57K, TeX)
May 2, 96

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Abstract. The observed general timeasymmetric behavior of
macroscopic systemsembodied in the second law of thermodynamicsarises
naturally from timesymmetric microscopic laws due to the great disparity
between
macro and microscales. 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 timeasymmetric 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. \bigskip \bigskip
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