Riccardo Mannella — Università di Pisa #
Fluctuation-Blowing processes in Ocean-Atmosphere interaction and in non Hamiltonian phenomena: some results #
For Hamiltonian systems, the Statistical Mechanics tools for studying the large scale emerging phenomena from a underlying chaotic and complex dynamics, are quite ripe and well assessed. Among them, the Zwanzig projection approach is one of the most powerful and used, leading to important results, as the microscopic foundation of the Fluctuation Dissipation relation, and the Canonical equilibrium Density Function (see, for example, M. Bianucci et al., Phys. Rev. E 51, 3002 (1995)). Actually, the projection approach leads at a calculus with differential operators that is usually almost intractable,  but that is drastically simplified when the basic dynamics of the system of interest is Hamiltonian, for which stadard Fluctuation Dissipation Relation holds true. In many real physical cases, however, the fundamental equations are not Hamiltonian. This happens, for example, in Fluid Dynamics, where the physics is described by the Navier Stokes Equations, or in Biology in general, just to cite a couple among many research fields. Here we show how it is still possible to get, in the non Hamiltonian case, a Generalized Fokker Planck Equation describing the time large scale statistics of a part of interest of the whole complex system. As an example, we focus our attention on the El Ni\~no Southern Oscillation, where a non standard Fluctuation Dissipation process plays a fundamental role.