Deriving thermodynamics from linear dissipativity theory
2016 (English)In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2016, 537-542 p.Conference paper (Refereed)Text
Complete and rigorous foundations for basic thermodynamic laws from the statistical description of microscopic systems has been a long-standing goal for mathematicians and physicists alike since Boltzmann. In this paper, we show how Willems's dissipativity theory provides a convenient framework to study a physical system at both microscopic and macroscopic level, and suggests a natural storage function different from the usual free energy to derive the theorem of energy equipartition of energy for linear systems. In this setup, we introduce a simple and general definition for temperature defined also out of equilibrium which allows to test the limits of validity of Fourier's law describing the transfer of heat from hot systems to cold systems. In particular under time-scale separation conditions, we derive the Maxwell-Cattaneo law, allowing for instantaneous flow of energy from cold to hot systems, which should be considered instead of Fourier's law for a proper description of energy exchanges between interconnected linear systems.
Place, publisher, year, edition, pages
IEEE conference proceedings, 2016. 537-542 p.
IdentifiersURN: urn:nbn:se:kth:diva-188284DOI: 10.1109/CDC.2015.7402284ScopusID: 2-s2.0-84962007668ISBN: 9781479978861OAI: oai:DiVA.org:kth-188284DiVA: diva2:936774
54th IEEE Conference on Decision and Control, CDC 2015, 15 December 2015 through 18 December 2015
QC 201606142016-06-142016-06-092016-06-14Bibliographically approved