What is the physical significance of chemical potential & fugacity?

Chemical Potential: Change in Gibbs free energy at const T & PFugacity: How much chemical potential of a phase differ from its standard state and its equal to partial pressure in case of ideal gas

Chemical Potential strictly speaking tells you in which direction the reaction will proceed, (negative = direct sens ; positive = indirect sense )

Fugacity  is derived from Chemical potential, in an applied definition, is the correction of the pressure of a non ideal gas.