Symplectic Structure of Information Geometry: Fisher Metric and EulerPoincaré Equation of Souriau Lie Group Thermodynamics  Frédéric Barbaresco

Author: Frédéric Barbaresco
DOI URL: http://dx.doi.org/10.1007/9783319250403_57
Video: http://www.youtube.com/watch?v=wTxIdmALzjo
Slides: Barbaresco_symplectic structure.pdf
Presentation: https://www.see.asso.fr/node/14339
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through coadjoint action of a group on its momentum space, defining physical observables like energy, heat, and momentum as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. In the framework of Lie Group Thermodynamics, an EulerPoincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant PoincaréCartanSouriau integral. Finally, we conclude on Balian Gauge theory of Thermodynamics compatible with Souriau’s Model.