Coauthors L. Bertini, A. De Sole, D. Gabrielli, C. Landim
Thermodynamic transformations connecting nonequilibrium stationary states have the peculiarity of dissipating, to keep the system out of equilibrium, an amount of energy which diverges for a quasi static transformation. By subtracting the divergent part one can define a renormalized work that satisfies a Clausius type inequality and with respect to which quasi static transformations are optimal. A different way of analyzing the energy balance and optimality criteria is to consider transformations over a long but finite time T developing the total work and the dissipated energy in powers of 1/T. The diverging terms cancel and one obtains relations among finite quantities.
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