Irreversibility of Linear Maps in terms of Subjectivity & Geometry

Abstract: In both classical and quantum physics, irreversible processes are described by maps that contract the space of states. The change in volume has often been taken as a natural quantifier of the amount of irreversibility. In Bayesian inference, loss of information results in the retrodiction for the initial state becoming increasingly influenced by the choice of reference prior. In this paper, we import this latter perspective into physics, by quantifying the irreversibility of any process with its Bayesian subjectivity; that is, the sensitivity of its retrodiction to one's prior. We show that this measure not only coheres with other figures of merit for irreversibility, but also has joint monotonicities with physically noteworthy information geometric measures.