A port-Dirac formulation for thermodynamics of non-simple systems⁎H.Y. is in part supported by JST CREST Grant Number JP-MJCR1914, the MEXT Top Global University Project, Waseda University (SR 2021C-134), JSPS Grant-in-Aid for Scientific Research (17H01097) and the Organization for University Research Initiatives. Issue 19 (2021)

• Record Type: Journal Article
• Authors: Yoshimura, Hiroaki; Gay-Balmaz, François
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 19(2021)
• Page Start: 32
• Page End: 37
• Publication Date: 2021
• Subjects: Dirac structures -- Non-simple systems -- Nonequilibrium thermodynamics -- Adiabatic piston -- Electric circuit; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.11.051
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: The paper presents a port-Dirac formulation for thermodynamics of non-simple systems, in which we consider a non-simple system whose thermodynamic states may be represented by several entropy variables. Here we regard such a non-simple system as an interconnected system with ports that can be represented by a port-Dirac system in the context of Dirac structures. We first show some extension of the Lagrange-d'Alembert principle for obtaining the evolution equations of such non-simple systems. Then, a Dirac structure is constructed on the Pontryagin bundle over a thermodynamic configuration manifold. Further, a port-Dirac dynamical formulation for such non-simple systems is demonstrated, where the developed evolution equations are to be equivalent with the generalized Lagrange-d'Alembert equations. The validity of the proposed approach is finally illustrated by two examples of an adiabatic piston and a resistive circuit with entropy production.