Optimizing work output for finite-sized heat reservoirs: Beyond linear response.

Abstract

We uncover an optimization principle for the finite-time heat-work conversion process performed between two finite-sized heat reservoirs in the nonlinear response regime that is characterized by rather generic flux-force relations. We solve the problem of maximizing work output in a given time interval by means of the variational method. Moreover, in the limiting case that the cold reservoir is infinite, we find the corresponding optimized process can be determined by a single quantity, which plays the role similar to that of the Hamiltonian in classical mechanics. Some theoretical implications are discussed consequently, under the generalized tight-coupling condition which applies to both linear and nonlinear response cases. Our results can hopefully help design and control realistic thermodynamical processes.