Integrability criterion for lowering of ionization potentials and formulation of the solution of the inverse problem of constructing consistent thermodynamic functions of nonideal plasmas

Within the chemical picture, it is shown that self-consistent Coulomb nonideality corrections that satisfy Maxwell's thermodynamic identities can be constructed from formulas for lowering of ionization potentials, obtained from plasma electrostatic microfields or derived in ad hoc or empirical fashion, provided that a necessary integrability criterion is satisfied. The solution of such an inverse problem is formulated and introduced in terms of a simple integral that gives the correction to Helmholtz free energy function. The required integrability criterion is derived and applied to investigate the thermodynamic consistency of some models in the literature. Maintaining the same functional dependence on species densities as in the original models, a routine to fix thermodynamic inconsistencies found in some of these models is introduced. The advantages and usefulness of such a reverse scheme are discussed.