Entropy 2005, 7[1], 1-14
ISSN 1099-4300

Lagrangian submanifolds generated by the Maximum Entropy principle

Marco Favretti

Dipartimento di Matematica Pura ed Applicata, Università di Padova,
via Belzoni, 7 -- 35131 Padova Italy
E-mail: favretti@math.unipd.it

Received: 25 October 2004 / Accepted: 12 January 2005 / Published: 12 January 2005

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.

PACS codes: 5.20Gg; 5.50.+q; 5.70.Fh

MSC 2000 codes: 53D12; 62B10; 82B20

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