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From Second Law Violations to Continuum Mechanics

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Continuous Media with Microstructure 2

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Abstract

The violations of the Second Law become relevant as the length and/or time scales become very small. The Second Law then needs to be replaced by the fluctuation theorem and, mathematically, the irreversible entropy evolves as a submartingale. Next, a framework thermomechanics relying on stochastic functionals of energy and entropy is outlined. This allows a study of diffusion-type problems with random field constitutive coefficients not required to satisfy the positive definiteness everywhere. Finally, a formulation of stochastic micropolar fluid mechanics is developed, accounting for the lack of symmetry of stress tensor on molecular scales.

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Acknowledgments

Constructive comments of the reviewers are appreciated. This work was partially supported by the NSF under grants IIP-1362146 and CMMI-1462749.

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Authors and Affiliations

  1. Department of Mechanical Science & Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Martin Ostoja-Starzewski

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  1. Martin Ostoja-Starzewski
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Correspondence to Martin Ostoja-Starzewski .

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Editors and Affiliations

  1. Faculty of Engineering, University of Duisburg-Essen, Essen, Germany

    Bettina Albers

  2. Poznan University of Technology, Faculty of Civil and Environmental Engin, Poznań, Poland

    Mieczysław Kuczma

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Ostoja-Starzewski, M. (2016). From Second Law Violations to Continuum Mechanics. In: Albers, B., Kuczma, M. (eds) Continuous Media with Microstructure 2. Springer, Cham. https://doi.org/10.1007/978-3-319-28241-1_12

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  • DOI: https://doi.org/10.1007/978-3-319-28241-1_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28239-8

  • Online ISBN: 978-3-319-28241-1

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