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 II) (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) submani...

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Bibliographic Details
Published inJournal of functional analysis Vol. 227; no. 1; pp. 227 - 243
Main Author Favretti, Marco
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2005
Subjects
Lagrange multipliers
Maximum Entropy Principle
Morse family
Onsager relations
Symplectic geometry
Maximum Entropy Principle
Morse family
Lagrange multipliers
Symplectic geometry
Onsager relations
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Summary:We show that the Maximum Entropy Principle (MEP) (Phys. Rev. 106 (Part I and II) (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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2004.12.003