title: Dissipative open systems theory as a foundation for the thermodynamics of linear systems.
abstract: In this paper, we advocate the use of open dynamical systems, i.e. systems sharing input and output variables with their environment, and the dissipativity theory initiated by Jan Willems as models of thermodynamical systems, at the microscopic and macroscopic level alike. We take linear systems as a study case, where we show how to derive a global Lyapunov function to analyse networks of interconnected systems. We define a suitable notion of dynamic non-equilibrium temperature that allows us to derive a discrete Fourier law ruling the exchange of heat between lumped, discrete-space systems, enriched with the Maxwell-Cattaneo correction. We complete these results by a brief recall of the steps that allow complete derivation of the dissipation and fluctuation in macroscopic systems (i.e. at the level of probability distributions) from lossless and deterministic systems.This article is part of the themed issue 'Horizons of cybernetical physics'.
authors.affiliation: Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM) and Center for Operations Research and Econometrics (CORE), Université catholique de Louvain, 4 Avenue Lemaître, 1348 Louvain-la-Neuve, Belgium jean-charles.delvenne@uclouvain.be.
authors.forename: Jean-Charles
authors.identifier: http://orcid.org/0000-0003-2356-7790
authors.initials: JC
authors.lastname: Delvenne
authors.affiliation: KTH Royal Institute of Technology, Osquldas väg 10, 100 44 Stockholm, Sweden.
authors.forename: Henrik
authors.initials: H
authors.lastname: Sandberg
keywords: Maxwell–Cattaneo; dissipation; entropy; linear systems; second law