Reinaldo Garc{í}a-Garc{í}a
By introducing the concept of "internal protocols", we extend the definition of non-adiabatic entropy production given for Markovian systems in [M. Esposito C. and Van den Broeck, Phys. Rev. Lett. \textbf{104} 090601, (2010)], to arbitrary non-Markov ergodic dynamics. This quantity satisfies an integral fluctuation theorem, leading to an extension of the second law of thermodynamics for transitions between certain non-steady states. It also can be written as a sum of generalized fluxes and forces, thus being suitable for thermodynamics. In the absence of internal protocols, one recovers the integral fluctuation theorem for the non-adiabatic entropy production and the second law of thermodynamics for transitions between non-equilibrium steady-states, exactly as for Markovian systems. On the other hand, the generalized fluctuation-dissipation relation also holds, clarifying that the necessary condition for it is ergodicity instead of Markovianity. We express our fluctuation theorem in terms of the true non-adiabatic entropy production and a violation term, which we explicitly identify. Our results are illustrated by studying two simple non-Markovian systems.
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http://arxiv.org/abs/1205.3577
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