Towards Continuum Mechanics with Spontaneous Violations of the Second Law of Thermodynamics

  • Martin Ostoja-Starzewski
  • Bharath V. Raghavan
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)


As dictated by modern statistical physics, the second law is to be replaced by the fluctuation theorem (FT) 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 a formulation of stochastic continuum thermomechanics, where the entropy evolves as a submartingale while the dissipation function is consistent with the FT. A summary is then given of the behavior of an atomic fluid in Couette flow, studied using a combination of kinetic theory, hydrodynamic theory, and molecular dynamics. Overall, the developed framework may be applied in many fields involving fluid flow and heat conduction on very small spatial scales.


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This material is based upon work partially supported by the NSF under grants CMMI-1462749 and IIP-1362146 (I/UCRC on Novel High Voltage / Temperature Materials and Structures).


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Martin Ostoja-Starzewski
    • 1
  • Bharath V. Raghavan
    • 1
  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA

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