Fluctuation formulas for the external potential v(r) are introduced in a modified Legendre-transformed representation of the density functional theory of electronic structure (isomorphic ensemble). A new (nuclear/geometric) reactivity index h(r), having the same status as the electronic Fukui function in the canonical ensemble, is thereby identified, h(r)=(1/N)[delta mu/delta sigma(r)](N,T)=(1/kT)[(mu.v(r))-(mu)(v(r))], where mu is the electronic chemical potential, sigma is the shape factor of the electron density distribution, N is the number of electrons, (...) denotes the ensemble average of a quantity, and (v(r)) is the ensemble averaged external potential. This new local quantity is shown to be an inverse of the local softness, and to provide a useful definition of a local hardness.