Optimal finite-time endoreversible processes

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Abstract
We treat the general problem of transferring a system from a given initial state to a given final state in a given finite time such that the produced entropy or the loss of availability is minimized. We give exact equations for the optimal process for the general case of a system with several state variables. For linear processes, e.g., in the limit of slow processes or if the Onsager coefficients do not depend on the fluxes, we find a constant entropy production rate or constant loss rate of availability. An alternative kinetic process length is introduced. The entropy production rate is the square of the speed based on this length and clock time. This length adequately treats variations of the system time scale matrix along the path. For the nonlinear case, the entropy production rate or loss rate of availability is generally not constant for an optimal process.