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Open systems and time reversal

Abstract In this paper we address the question of the direction of physical time. In particular we consider the meaning of time reversal for irreversible evolution. The work is based on the theory of Markovian generators in open quantum systems. The motivation and appearance of such evolution is reviewed and its implications for the direction of time are presented. A monotonically changing function, a Lyapunov functional, is demonstrated and the concept of time reversal invariance is introduced. Finally the evolution is shown to follow from an action principle. The method, however, does not single out any forward direction of time, information about the initial state is lost equally in both directions within the formalism.