Fluctuation relations and positivity of the entropy production in irreversible dynamical systems

Abstract

We give a generalization of fluctuation identities and inequalities for the entropy production when the microscopic dynamics preserves the phase space volume but is not assumed to be dynamically reversible. We find that general first properties such as the strict positivity of the entropy production or the validity of an H-theorem are unaffected by the irreversibility of the dynamics. Fluctuation identities describing the relation between entropy production and its time-reversal must, however, be changed and now involve the time-reversed dynamics.