Approach to equilibrium in the Fokker-Planck equation for Hamiltonian systems

The aim of the project is to see how a system in contact with a thermal bath approaches equilibrium, described by the canonical ensemble density (Gibbs density). The physical system has been modeled with the use of stochastic and dissipative contributes: it has been studied the evolution of the norm (in Gibbs measure) of the deviation from equilibrium, and the trend of the free energy of the system. Particular regard has been given to the case of noise present only at the surface of the solid object. It was possible to obtain an estimation of the characteristic time of equilibrium for such systems.