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.
Isotropic submanifolds generated by the Maximum Entropy principle and Onsager reciprocity relations
FAVRETTI, MARCO
2005
Abstract
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.
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