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 dynam¬ics. From this formulation we deduce minimal dissipation principles, dynamical inclusions, or constrained evolution with hamiltonian drift reformulations. Among applications we recover a dynamics generaliza¬tion 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 [3] arXiv:0810.1419, then in [4] arXiv:1408.3102 and, for the ap¬pearance of bipotentials in relation to the symplectic duality, in [2] arXiv:1902.04598v1."