Continuum physics with violations of the second law of thermodynamics

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

As dictated by the modern statistical physics, the second law is to be replaced by the fluctuation theorem on very small length and/or time scales. This means that the deterministic continuum thermomechanics must be generalized to a stochastic theory allowing randomly spontaneous violations of the Clausius–Duhem inequality to take place anywhere in the material domain. This paper outlines possible extensions of stochastic continuum thermomechanics in coupled field problems: (i) thermoviscous fluids, (ii) thermo-elastodynamics, and (iii) poromechanics with dissipationwithin the skeleton, the fluid, and the temperature field. Linear dissipative processes are being considered, with the thermodynamic orthogonality providing the average constitutive response and the fluctuation theorem providing the violations of the second law of thermodynamics. Special attention is paid to the fact that one can develop hyperbolic theories (i.e. free of the paradox of infinite speeds of signal transmission) while working with the Fourier-type conduction for which the fluctuation theorem has already been developed.

Original languageEnglish (US)
Title of host publicationMathematical Modelling in Solid Mechanics
EditorsMircea Sofonea, Francesco dell’Isola, David Steigmann
PublisherSpringer-Verlag Berlin Heidelberg
Pages181-192
Number of pages12
ISBN (Print)9789811037634
DOIs
StatePublished - Jan 1 2017
EventInternational conference on Emerging Trends in Applied Mathematics and Mechanics, ETAMM 2016 - Perpignan, France
Duration: May 30 2016Jun 3 2016

Publication series

NameAdvanced Structured Materials
Volume69
ISSN (Print)1869-8433
ISSN (Electronic)1869-8441

Other

OtherInternational conference on Emerging Trends in Applied Mathematics and Mechanics, ETAMM 2016
CountryFrance
CityPerpignan
Period5/30/166/3/16

ASJC Scopus subject areas

  • Materials Science(all)

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  • Cite this

    Ostoja-Starzewski, M. (2017). Continuum physics with violations of the second law of thermodynamics. In M. Sofonea, F. dell’Isola, & D. Steigmann (Eds.), Mathematical Modelling in Solid Mechanics (pp. 181-192). (Advanced Structured Materials; Vol. 69). Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/978-981-10-3764-1_12