TY - GEN

T1 - Continuum physics with violations of the second law of thermodynamics

AU - Ostoja-Starzewski, Martin

N1 - Funding Information:
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).

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

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U2 - 10.1007/978-981-10-3764-1_12

DO - 10.1007/978-981-10-3764-1_12

M3 - Conference contribution

AN - SCOPUS:85015837932

SN - 9789811037634

T3 - Advanced Structured Materials

SP - 181

EP - 192

BT - Mathematical Modelling in Solid Mechanics

A2 - Sofonea, Mircea

A2 - dell’Isola, Francesco

A2 - Steigmann, David

PB - Springer-Verlag Berlin Heidelberg

T2 - International conference on Emerging Trends in Applied Mathematics and Mechanics, ETAMM 2016

Y2 - 30 May 2016 through 3 June 2016

ER -