Dissipation and the information content of the deviation from hamiltonian dynamics

Abstract: We explain a dissipative version of hamiltonian mechanics, based on the information content of the deviation from hamiltonian dynamics. From this formulation we deduce minimal dissipation principles, dynamical inclusions, or constrained evolution with hamiltonian drift reformulations. Among applications we recover a dynamics generalization of Mielke et al quasistatic rate-independent processes. This article gives a clear and unitary presentation of the theory of hamiltonian inclusions with convex dissipation or symplectic Brezis-Ekeland-Nayroles principle, presented under various conventions first in arXiv:0810.1419, then in arXiv:1408.3102 and, for the appearance of bipotentials in relation to the symplectic duality, in arXiv:1902.04598v1.