If the change in this quantity is negative for a reaction, the reaction is spontaneous; a zero change implies equilibrium.  
The isothermal pressure partial derivative of this state function is equal to the isentropic pressure partial derivative of the enthalpy; a fact useful in deriving Maxwell's relations.  It is constant along a coexistence line in a state diagram, and is logarithmically related to a reaction's equilibrium constant.  If the change in this quantity is negative for a reaction, the reaction is spontaneous; a zero change implies equilibrium.  Defined differentially as the maximum attainable work of an open system, FTP, identify this state function that may be simply defined as the enthalpy minus the product of temperature and entropy and that is named for an American scientist.
The isothermal pressure partial derivative of this state function is equal to the isentropic pressure partial derivative of the enthalpy; a fact useful in deriving Maxwell's relations.  
Gibbs free energy (or Gibbs function or Gibbs potential function; prompt on "free energy" or "G" or "g")