  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.
