### Abstract

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.

Original language | English (US) |
---|---|

Title of host publication | Advanced Structured Materials |

Publisher | Springer-Verlag |

Pages | 633-640 |

Number of pages | 8 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Advanced Structured Materials |
---|---|

Volume | 89 |

ISSN (Print) | 1869-8433 |

ISSN (Electronic) | 1869-8441 |

### Fingerprint

### ASJC Scopus subject areas

- Materials Science(all)

### Cite this

*Advanced Structured Materials*(pp. 633-640). (Advanced Structured Materials; Vol. 89). Springer-Verlag. https://doi.org/10.1007/978-3-319-72440-9_33

**Towards continuum mechanics with spontaneous violations of the second law of thermodynamics.** / Starzewski, Martin Ostoja; Raghavan, Bharath V.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advanced Structured Materials.*Advanced Structured Materials, vol. 89, Springer-Verlag, pp. 633-640. https://doi.org/10.1007/978-3-319-72440-9_33

}

TY - CHAP

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

AU - Starzewski, Martin Ostoja

AU - Raghavan, Bharath V.

PY - 2018/1/1

Y1 - 2018/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85044655693&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044655693&partnerID=8YFLogxK

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-Verlag

ER -