TY - CHAP

T1 - Towards continuum mechanics with spontaneous violations of the second law of thermodynamics

AU - Ostoja-Starzewski, Martin

AU - Raghavan, Bharath V.

N1 - Funding Information:
Acknowledgements 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).
Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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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U2 - 10.1007/978-3-319-72440-9_33

DO - 10.1007/978-3-319-72440-9_33

M3 - Chapter

AN - SCOPUS:85044655693

T3 - Advanced Structured Materials

SP - 633

EP - 640

BT - Advanced Structured Materials

PB - Springer

ER -