Lagrangian submanifolds generated by the Maximum Entropy principle

Abstract

We show that the Maximum Entropy principle (E.T. Jaynes, [8]) has a natural description in terms of Morse Families of a Lagrangian submanifold. This geometric approach becomes useful when dealing with the M.E.P. with nonlinear constraints. Examples are presented using the Ising and Potts models of a ferromagnetic material.

Keywords

• symplectic geometry
• maximum entropy principle
• thermodynamics of mechanical systems
• Ising and Potts models