Abstract
This paper deals with Jean-Louis Koszul’s works related to Geometric and Analytic Mechanics, and to Souriau’s Lie Group Thermodynamics that have appeared over time as elementary structures of Information Geometry. The 2nd Koszul form has been extended by Jean-Marie Souriau in his Symplectic model of Statistical Physics called “Lie Groups Thermodynamics” providing an extension of Fisher metric for homogeneous Symplectic manifolds, associated to KKS (Kirillov-Kostant-Souriau) 2-form in case of non-null cohomology. Jean-Louis Koszul has developed mathematical foundation of Souriau model in the Lecture “Introduction to Symplectic Geometry”.
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