Generalized Thermodynamics of Maximum Work in Finite Time

We consider thermodynamic behaviour of thermal machines founded on kinetic rather than static origins. Their models, which are formulated for finite time transitions, simplify to models of classical thermodynamics in the limiting case of an infinite duration. An extended exergy is derived as a finite-time extension of the classical thermodynamic work delivered from a system of a body and its environment. With this quantity enhanced bounds can be determined for active continuous and cascade processes, in which there is an indirect energy exchange between two sybsystems through the working fluid of an engine, a refrigerator or a heat pump. These bounds refer to systems with finite exchange area or with a finite contact time. An economic framework of this theory is outlined.For both continuous and discrete processes, nonlinear thermodynamic models are derived from a combination of the energy balance and transfer equations. These models serve as constraints in the problem of work optimization. Variational and optimal control approaches are developed which are analogous to those found in analytical mechanics. Variational calculus is used along with some aspect of the canonical transformation theory to maximize work and discuss the role of a finite process intensity and of a finite duration.The optimality of a definite irreversible process for a finite-time transition of a controlled fluid is pointed out as well as a connection between the process duration, optimal dissipation and the optimal process intensity measured in terms of a hamiltonian, a dissipative quantity. It is shown that limits of the classical availability theory should be replaced by stronger limits which are obtained for finite time processes, and which are closer to reality. A hysteretic property of the generalized exergy describes a decrease of the maximum work received from an engine system and an increase of work added to a heat pump system, the features which are particularly important in high-rate regions of thermodynamic processes. For an infinite sequence of infinitesimal thermal machines, an optimal temperature strategy is obtained in the form similar to that known in the theory of simulated annealing.