Generalized Clausius relation and power dissipation in nonequilibrium stochastic systems

In the framework of the stochastic dynamics of open Markov systems, we derive an extension of the Clausius inequality for transitions between states of the system. We give a formula for the power produced when the system is in its stationary state and relate it to the dissipation of energy needed to maintain the system out of equilibrium. We deduce that, near equilibrium, maximal power production requires an energy dissipation of the same order of magnitude as the power production.