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Dissipative open systems theory as a foundation for the thermodynamics of linear systems
KTH, School of Electrical Engineering (EES), Automatic Control.
2017 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 375, no 2088, 20160218Article in journal (Refereed) Published
Abstract [en]

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'.

Place, publisher, year, edition, pages
2017. Vol. 375, no 2088, 20160218
Keyword [en]
linear systems, dissipation, second law, entropy, Maxwell-Cattaneo
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-203144DOI: 10.1098/rsta.2016.0218ISI: 000393413200010OAI: oai:DiVA.org:kth-203144DiVA: diva2:1081298
Note

QC 20170313

Available from: 2017-03-13 Created: 2017-03-13 Last updated: 2017-03-13Bibliographically approved

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