Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

I will show some of the basic tools in symplectic and Poisson geometry with applications to thermodynamics and statistical physics. The basic concepts of thermodynamics like the notion of equilibrium, entropy or Gibbs statistical states may be expressed in terms of differential geometry in a nice and elegant way. I will show how the concept of the Gibbs state may be generalised for a Hamiltonian action of a Lie group on the symplectic manifold representing the system. The examples of the applications in physics will be given