A deficit function is introduced into the conventional treatment of the Second Law of Thermodynamics, by which one may relate the heat and work exchanges for irreversible processes to those of reversible processes. The conventional formulations for functions of state may then be generalized to cases where the intensive variables of the system and its surroundings differ to an arbitrary extent. This permits the contribution of irreversible processes to the total entropy to be specified in terms of experimentally accessible parameters.
Honig et al. (Sat,) studied this question.