Open Markov processes: A compositional framework for non-equilibrium steady states.

Open Markov processes are generalizations of Markov processes in which probability can flow in and out of the system through some set of boundary states. We present a framework in which open Markov processes are morphisms in a category. Composition in this category provides a systematic way of constructing larger systems by composing smaller open systems. We describe a `black-box functor' which characterizes non-equilibrium steady states of open Markov processes in terms of the steady state flows of probability through the system.