Isotropic submanifolds generated by the Maximum Entropy principle and Onsager reciprocity relations

We show that the Maximum Entropy Principle (MEP) (Phys. Rev. 106 (Part I and 11) (1957) 620-630; Phys. Rev. 108 (1957) 171-630), when considered as a constrained extremization problem, defines in a natural way a Morse Family and a related isotropic (Lagrangian in the finite-dimensional case) submanifold of an infinite-dimensional linear symplectic space. This geometric approach becomes useful when dealing with the MEP with nonlinear constraints and it allows to derive Onsager-like reciprocity relations as a consequence of the isotropy.