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Optimal thermodynamic processes in out-of-equilibrium systems


The second law of Thermodynamics imposes severe limitations to the energetic cost of manipulations of physical systems. The minimal cost is only achieved in principle for extremely slow processes which are not feasible in real conditions. Thus, it is mandatory to approach the following problem: which is the thermodynamic process that, in finite time, minimizes the energetic cost of a given manipulation? The corresponding solution is still restrict to very few examples. Although there exists a preliminar theory that applies to a very general class of systems, it is only capable of describing restricted out-of-equilibrium regimes. The present proposal aims to contribute for the solution of this optimisation problem applied to classical or quantum systems in contact with or isolated from a thermal reservoir. The costs in finite time will be quantified either by the thermodynamic work or by entropy production according to the application. From the theoretical point of view, the appropriated tools must yield a formulation of such quantifiers as functionals of the driving protocol. This is something that has been done in our research group at least using perturbative methods for close-to-equilibrium processes. This previous knowledge will be the starting point for a treatment of arbitrarily out-of-equilibrium processes. The desired results will certainly have impact on the analysis of efficiency of mesoscopic thermal engines and on the restrictions imposed by the second law in finite time. (AU)