Form of uncompensated heat giving rise to a Pfaffian differential form in thermodynamic space

A form of uncompensated heat is presented which gives rise to a Pfaffian differential form for a non- equilibrium extension of equilibrium entropy when the thermodynamic space is broadened to include fluxes of various orders. It is thereby shown that the Pfaffian form descends from the Clausius inequality, which is regarded as equivalent to the second law of thermodynamics