On the Generating Functions of Irreversible port-Hamiltonian Systems

TL;DR

This paper explores the geometric structure of irreversible port-Hamiltonian systems' drift dynamics, characterizing it through a covariant 4-tensor and conditions for reduction to quasi-Poisson brackets.

Contribution

It introduces a novel geometric framework for analyzing the drift dynamics of irreversible port-Hamiltonian systems using a covariant 4-tensor and reduction conditions.

Findings

Characterization of the drift dynamics via a covariant 4-tensor

Conditions for reducing the 4-tensor to a product of quasi-Poisson brackets

Insight into the interconnection structure of irreversible phenomena

Abstract

We study the geometric structure of the drift dynamics of Irreversible port-Hamiltonian systems. This drift dynamics is defined with respect to a product of quasi-Poisson brackets, reflecting the interconnection structure and the constitutive relations of the irreversible phenomena occuring in the system. We characterize this product of quasi-Poisson brackets using a covariant 4-tensor and an associated function. We derive various conditions for which this 4-tensor and the associated function may be reduced to a product of quasi-Poisson brackets.