Excess Grand Potential for a System under an External Field: Effects of External Field Driven Nonextensivity

We report that an external field can drive inherently extensive systems into nonextensive ones. For the correct grand canonical description of nonextensive systems, it is necessary to take into account the excess grand potential, X, in addition to the conventional grand potential proportional to the thermodynamic pressure, which has long been overlooked in the literature in this field. We present the statistical mechanical expression for X of a system as a functional of the external field imposed on the system, from which we establish the criterion for the external field that drives an inherently extensive macroscopic system into a nonextensive one.