### Abstract

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.

Original language | English (US) |
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Title of host publication | Mathematical Modelling in Solid Mechanics |

Editors | Mircea Sofonea, Francesco dell’Isola, David Steigmann |

Publisher | Springer-Verlag Berlin Heidelberg |

Pages | 181-192 |

Number of pages | 12 |

ISBN (Print) | 9789811037634 |

DOIs | |

State | Published - Jan 1 2017 |

Event | International conference on Emerging Trends in Applied Mathematics and Mechanics, ETAMM 2016 - Perpignan, France Duration: May 30 2016 → Jun 3 2016 |

### Publication series

Name | Advanced Structured Materials |
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Volume | 69 |

ISSN (Print) | 1869-8433 |

ISSN (Electronic) | 1869-8441 |

### Other

Other | International conference on Emerging Trends in Applied Mathematics and Mechanics, ETAMM 2016 |
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Country | France |

City | Perpignan |

Period | 5/30/16 → 6/3/16 |

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### ASJC Scopus subject areas

- Materials Science(all)

### Cite this

*Mathematical Modelling in Solid Mechanics*(pp. 181-192). (Advanced Structured Materials; Vol. 69). Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/978-981-10-3764-1_12