mdh.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Continuum Mechanics beyond the Second Law of Thermodynamics
University of Illinois in Urbana-Champaigne, USA.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics/Applied Mathematics)ORCID iD: 0000-0002-0139-0747
2014 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 1470, no 2171, p. 1-17, article id 20140531Article in journal (Refereed) Published
Abstract [en]

The results established in contemporary statistical physics indicating that, on very small space and time scales, the entropy production rate may be negative, motivate a generalization of continuum mechanics. On account of the fluctuation theorem, it is recognized that the evolution of entropy at a material point is stochastically (not deterministically) conditioned by the past history, with an increasing trend of average entropy production. Hence, the axiom of Clausius-Duhem inequality is replaced by a submartingale model, which, by the Doob decomposition theorem, allows classification of thermomechanical processes into four types depending on whether they are conservative or not and/or conventional continuum mechanical or not. Stochastic generalizations of thermomechanics are given in the vein of either thermodynamic orthogonality or primitive thermodynamics, with explicit models formulated for Newtonian fluids with, respectively, parabolic or hyperbolic heat conduction. Several random field models of the martingale component, possibly including spatial fractal and Hurst effects, are proposed. The violations of the second law are relevant in those situations in continuum mechanics where very small spatial and temporal scales are involved. As an example, we study an acceleration wavefront of nanoscale thickness which randomly encounters regions in the medium characterized by a negative viscosity coefficient.

Place, publisher, year, edition, pages
2014. Vol. 1470, no 2171, p. 1-17, article id 20140531
National Category
Other Physics Topics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-27325DOI: 10.1098/rspa.2014.0531ISI: 000360605300009Scopus ID: 2-s2.0-84988982017OAI: oai:DiVA.org:mdh-27325DiVA, id: diva2:781981
Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2017-12-05Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Malyarenko, Anatoliy

Search in DiVA

By author/editor
Malyarenko, Anatoliy
By organisation
Educational Sciences and Mathematics
In the same journal
Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences
Other Physics Topics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 47 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf