Mathematics Colloquium

Starting from properties of relative entropy I discuss examples of irreversible behavior observed in physical systems with seemingly timereversal invariant dynamics. (I limit my analysis to quantum-mechanical models of physical systems.) Among my examples are ones found inmodel systems for which the second Law of thermodynamics can be proven, models of quantum Brownian motion and models of quantum friction. I conclude with a brief discussion of the fundamental arrow of time found in quantum mechanics.