# Entropy changes for steady-state fluctuations

## Abstract

The dissipative steady state far from equilibrium and subject to a slow modulation of external parameters is analyzed. It is shown that the time-integrated energy dissipation consists of three terms. The first of these is irreversible and consists of the time-integrated dissipation of the sequence of exact steady states defined by the externally controlled parameters traversed during the modulation. The second term is reversible and reflects the fact that the dissipation of the time-dependent modulated system, as calculated in a macroscopic way from ensemble averages, is not the same as the dissipation of a sequence of exact steady states. The third term is also reversible and relates to the ensemble dispersion in changes in stored energy during the modulation. If the system has a single degree of freedom and narrow fluctuations, then these fluctuations can be characterized by an effective temperature TN. The third term can then be shown to be equal to TN dS, where S is the entropy calculated from the distribution function by the usual definition. © 1973 Plenum Publishing Corporation.