The Rectified Second Law of Thermodynamics^†

Equilibrium thermodynamics is combined with Jarzynski's irreversible work theorem to quantify the excess entropy produced by irreversible processes. The resulting rectified form of the second law parallels the first law, in the sense that it facilitates the experimental measurement of excess entropy changes resulting from irreversible work and heat exchanges, just as the first law quantifies energy changes produced by either reversible or irreversible work and heat exchanges. The general form of the rectified second law is further applied to a broad class of quasi-static irreverisble (QSI) processes, for which all of the thermodynamic functions of both the system and surroundings remain continuously well-defined, thus facilitating excess entropy measurements by integrating exact differential functions along QSI paths. The results are illustrated by calculating the mechanical and thermal excess entropy produced by the irreversible unfolding of an RNA molecule.