Christian Maes, Karel Netocny
Time-reversal and Entropy
(377K, Postscript)
ABSTRACT. There is a
relation between the irreversibility of thermodynamic processes as
expressed by the breaking of time-reversal symmetry, and the
entropy production in such processes. We explain on an elementary
mathematical level the relations between entropy production,
phase-space contraction and time-reversal starting from a
deterministic dynamics. Both closed and open systems, in the
transient and in the steady regime, are considered. The main
result identifies under general conditions the statistical
mechanical entropy production as the source term of time-reversal
breaking in the path space measure for the evolution of reduced
variables. This provides a general algorithm for computing the
entropy production and to understand in a unified way a number of
useful (in)equalities. We also discuss the Markov approximation.
Important are a number of old theoretical ideas for connecting the
microscopic dynamics with thermodynamic behavior.