Thermodynamics in finite time. II. Potentials for finite-time processes

Within the context of conventional time-independent thermodynamics, an algorithm is developed to construct potentials $\mathcal{P}$ that define the extremal values of work for processes with arbitrary constraints. An existence theorem is proved that demonstrates that such potentials $\mathcal{P}$ can be given for any quasistatic process. This theorem extends the capability of thermodynamics from reversible processes to one class of time-dependent processes. A corollary shows how such potentials can be constructed for systems whose time dependence is first order. A final theorem shows the equivalence of the extremal work derived by solution of an optimal control problem with the work derived as a change in the generalized potentials, $\Delta \mathcal{P}$. Examples are given to illustrate the constructions.