Abstract - Classical/Stochastic Geometric Mechanics and Lie Group Thermodynamics /Statistical Physics
List of speakers :
- Frédéric Barbaresco Thales Air Systems. Limours, France.
- Joël Bensoam Ircam, centre G. Pompidou, CNRS UMR 9912, Paris, France.
- François Gay-Balmaz LMD - Ecole Normale Supérieure de Paris, Paris, France.
- Frédéric Hélein Institut de Mathématiques de Jussieu, Paris, France.
- Bernhard Maschke Claude Bernard University Lyon 1, LAGEP, Villeurbanne, France.
This session will explore a unifying framework for Classical/Stochastic Geometric Mechanics and Statistical Physics, based on Symplectic and Multi-Symplectic Geometry and Lie Group Theories. Jean- Marie Souriau has introduced a “Lie Group Thermodynamics” in Statistical Physics and “Continuous Medium Thermodynamics” that could beneficiate of most recent works from Geometric Mechanics and its most recent stochastic developments. In particular, the conservation laws (or more generally the circulation invariants: Noether’s currents) that derive from the underlying symmetries of Lie groups allow reducing the Partial Differential Equations (PDEs) problems. Other approaches will be considered as Euler-Poincaré reduction theorem for stochastic processes taking values in a Lie group, which is a generalization of the Lagrangian version of reduction and its associated variational principles. The objective is to embrace common principles for all the changes of state of the body , both the change of place and the change of physical qualities extended to the case of incomplete knowledge and random uncertainties.