In this paper, we present a generalized entropy criterion for solving the rational Nevanlinna-Pick problem for n + 1 interpolating conditions and the degree of interpolants bounded by n, The primal problem of maximizing this entropy gain has a very well-behaved dual problem. This dual is a convex optimization problem in a finite-dimensional space and gives rise to an algorithm for finding all interpolants which are positive real and rational of degree at most n, The criterion requires a selection of a monic Schur polynomial of degree n, It follows that this class of monic polynomials completely parameterizes all such rational interpolants, and it therefore provides a set of design parameters for specifying such interpolants. The algorithm is implemented in state-space form and applied to several illustrative problems in systems and control, namely sensitivity minimization, maximal power transfer and spectral estimation.