Metriplectic Euler-Poincaré equations: smooth and discrete dynamics - Anthony Bloch; Marta Farré Puiggalí; David Martín de Diego (Communications in Analysis and Mechanics)
In this paper we will introduce a discrete version of systems obtained by modifications of the Euler-Poincaré equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism. The metriplectic representation of the dynamics allows us to describe the conservation of energy, as well as to guarantee entropy production. For deriving the discrete equations we use discrete gradients to numerically simulate the evolution of the continuous metriplectic equations preserving their main properties: preservation of energy and correct entropy production rate.