Representation of irreversible systems in a metric thermodynamic phase space∗. Issue 8 (2015)

• Record Type: Journal Article
• Authors: Hudon, Nicolas; Dochain, Denis; Guay, Martin
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 8(2015)
• Page Start: 1070
• Page End: 1074
• Publication Date: 2015
• Subjects: Nonlinear systems -- metriplectic systems -- irreversible systems -- contact geometry; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.09.110
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper studies geometric properties of a class of irreversible dynamical systems, referred to in the literature as metriplectic systems. This class of systems, related to generalized (or dissipative) Hamiltonian systems, are generated by a conserved component and a dissipative component and appear, for example, in non-equilibrium thermodynamics. In non-equilibrium thermodynamics, the two potentials generating the dynamics are interpreted as generalized energy and generalized entropy, respectively. Stability and stabilization results for metriplectic systems have been presented in the literature, however, some aspects are still poorly understood, in particular the existence of dynamical invariants such as periodic orbits. In this note, we study the properties of metriplectic systems by considering a lift from the n-dimensional state space to a (2n+1)-dimensional contact space, following an approach introduced in recent years to study irreversible control systems. This lift leads to a deeper geometric characterization of metriplectic systems in the extended space. An example is provided to illustrate the approach proposed in this paper.