METRIPLECTIC FORMALISM: FRICTION AND MUCH MORE
Massimo F. D. Materassi, Philip J. Morrison
Metriplectic formalism is a construction based on an extension of Poisson brackets in which a Hamiltonian system is perturbed with dissipation, in order for it to converge to an asymptotic equilibrium. Phenomena as friction, electric resistivity, thermal conductivity and collisions in kinetic theories are well represented in this framework. Here the program is to extend the metriplectic formalism so to include convergence to non-zero dimensional attractors, e,g, limit cycles and strange attractors, in order for it to represent bio-physical, geophysical and ecological models. When this is done, the interpretation of the “Hamiltonian” and the “Free Energy” of the system is quite interesting.