Isotropic Submanifolds generated by the Maximum Entropy Principle

We show that the Maximum Entropy Principle (E.T. Jaynes, 1957) when considered as a constrained extremization problem, has a natural description in terms of Morse families of an isotropic (lagrangian in the finite-dimensional case) submanifold of an infinite-dimensional linear symplectic space. This geometric approach become useful when dealing with the MEP with nonlinear constraints and it allows to derive Onsager-like reciprocity relations as a consequence of the isotrop