:::The differential is actually right, because TR, PR and μR in the definition of Availability are all assumed to be fixed properties of the external surroundings, so there are no terms like SdTR.  Availability can be thought of as a generalisation of free energy, because the temperature in the definition is the external temperature TR, rather than the current temperature.  It's actually a generalisation of the Gibbs free energy, because the Availability function includes the term PRV so that differences in Availability measure the "useful" work, rather than the total work available; any work done merely to expand against the external pressure is not considered useful.