Work and power production in non-equilibrium systems

We study work production in a Markov system obeying discrete stochastic dynamics. As our main result, we establish a new equality concerning the work produced during a spontaneous transformation in an isothermal, non-equilibrium system. Then we consider the overall evolution of a non-equilibrium system driven by an external parameter and generalize Jarzynski's equality for systems maintained out of equilibrium. That equality is recovered if the initial and final state distributions are equilibriums.