The Jarzynski relation, fluctuation theorems, and stochastic thermodynamics for non-Markovian processes

We prove the Jarzynski relation for general stochastic processes including non-Markovian systems with memory. The only requirement for our proof is the existence of a stationary state, therefore excluding non-ergodic systems. We then show how the concepts of stochastic thermodynamics can be used to prove further exact non- equilibrium relations like the Crooks relation and the fluctuation theorem on entropy production for non-Markovian dynamics.