Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Continuum Mechanics with Spontaneous Violations of the Second Law of Thermodynamics

  • Martin Ostoja-StarzewskiEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_65-1

Synonyms

Definitions

With reference to contemporary statistical physics, random spontaneous violations of the second law of thermodynamics are relevant where/when the length and/or time scales become very small. A development of a stochastic continuum thermomechanics accounting for such violations through a fluctuation theorem is discussed. Several applications are reviewed.

Introduction

The recognition that irreversibility is stochastic dates back to J.C. Maxwell who said “the second law is of the nature of strong probability … not an absolute certainty”. The strong footing for this statement, however, has been established only recently, beginning with Evans et al. (1993). The ongoing research has been theoretical, simulational, and experimental (Evan and Searles 1994; Wang et al. 2002; Evans and Searles 2002; Carberry et al. 2004). It has been established that, in general,...

This is a preview of subscription content, log in to check access.

Notes

Acknowledgment

This material is based upon work partially supported by the NSF under grant CMMI-1462749.

References

  1. Carberry DM, Reid JC, Wang GM, Sevick EM, Searles DJ, Evans DJ (2004) Fluctuations and irreversibility: an experimental demonstration of a second-law-like theorem using a colloidal particle held in an optical trap. Phys Rev Lett 92(14):140601CrossRefGoogle Scholar
  2. Coussy O (2004) Poromechanics. Wiley, HobokenzbMATHGoogle Scholar
  3. Doob JL (1953) Stochastic processes. Wiley, New YorkGoogle Scholar
  4. Edelen DGB (1974) Primitive thermodynamics: a new look at the Clausius–Duhem inequality. Int J Eng Sci 12:121–141MathSciNetCrossRefGoogle Scholar
  5. Evan DJ, Searles DJ (1994) Equilibrium microstates which generate second law violating steady states. Phys Rev E 50(2):1645–1648CrossRefGoogle Scholar
  6. Evans DJ Morriss GP (2008) Statistical mechanics of nonequilibrium liquids. Cambridge University Press, CambridgeGoogle Scholar
  7. Evans DJ, Searles DJ (2001) Fluctuation theorem for heat flow. Int J Thermophys 22:123–134CrossRefGoogle Scholar
  8. Evans DJ, Searles DJ (2002) The fluctuation theorem. Adv Phys 51(7):1529–1585CrossRefGoogle Scholar
  9. Evans DJ, Cohen EGD, Morriss GP (1993) Probability of second law violations in steady states. Phys Rev Lett 71(15):2401–2404CrossRefGoogle Scholar
  10. Jarzynski C (2011) Equalities and inequalities: irreversibility and the second law of thermodynamics at the nanoscale. Ann Rev Condens Matter Phys 2:329–351CrossRefGoogle Scholar
  11. LAMMPS (2010) (“Large-scale atomic/molecular massively parallel simulator”), Sandia National LaboratoriesGoogle Scholar
  12. Malyarenko A, Ostoja-Starzewski M (2014) Statistically isotropic tensor random fields: correlation structures. Math Mech Compl Syst 2:209–231MathSciNetCrossRefGoogle Scholar
  13. Malyarenko A, Ostoja-Starzewski M (2016) Spectral expansions of homogeneous and isotropic tensor-valued random fields. ZAMP 67:59MathSciNetzbMATHGoogle Scholar
  14. Maugin GA (1999) The thermomechanics of nonlinear irreversible behaviors – an introduction. World Scientific, SingaporeCrossRefGoogle Scholar
  15. Muschik W (2016) Non-equilibrium equilibrium thermodynamics and stochasticity, a phenomenological look on Jarzynski’s equality. Continuum Mech Thermodyn 28(6):1887–1903. https://arxiv.org/abs/1603.02135MathSciNetCrossRefGoogle Scholar
  16. Ostoja-Starzewski M (2016) Second law violations, continuum mechanics, and permeability. Contin Mech Thermodyn 28:489–501. Erratum (2017) 29, 359MathSciNetCrossRefGoogle Scholar
  17. Ostoja-Starzewski M (2017a) Continuum physics with violations of the second law of thermodynamics In: dell’Isola F, Sofonea M, Steigmann D (eds) Proceedings ETAMM, 181–192, Springer, 2017. doi https://doi.org/10.1007/978-981-10-3764-1Google Scholar
  18. Ostoja-Starzewski M (2017b) Admitting spontaneous violations of the second law in continuum thermomechanics. Entropy 19:78.), 10 pages. https://doi.org/10.3390/e19020078CrossRefGoogle Scholar
  19. Ostoja-Starzewski M, Malyarenko A (2014) Continuum mechanics beyond the second law of thermodynamics. Proc R Soc A 470:20140531CrossRefGoogle Scholar
  20. Ostoja-Starzewski M, Raghavan B (2016) Continuum mechanics versus violations of the second law of thermodynamics. J Thermal Stress 39(6):734–749CrossRefGoogle Scholar
  21. Raghavan B, Ostoja-Starzewski M (2017a) Shear-thinning characteristics of molecular fluids undergoing planar Couette flow. Phys Fluids 29:023103-1-7. https://doi.org/10.1063/1.4976319CrossRefGoogle Scholar
  22. Raghavan B, Karimi P, Ostoja-Starzewski M (2017b) Stochastic characteristics and Second Law violations of atomic fluids in Couette flow. Phys A 496:90–107MathSciNetCrossRefGoogle Scholar
  23. Rivlin RS (1970) Red herrings and sundry unidentified fish in non-linear continuum mechanics. In: Kanninen A, Rosenfeld J (eds) Inelastic behavior of solids. McGraw-Hill, New York, pp 117–134Google Scholar
  24. Wang GM, Sevick EM, Mittag E, Searles DJ, Evans DJ (2002) Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. Phys Rev Lett 89:050601CrossRefGoogle Scholar
  25. Ziegler H (1983) An introduction to thermomechanics. Elsevier, North-HollandzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Department of Mechanical Science & Engineering, Institute for Condensed Matter Theory and Beckman InstituteUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Section editors and affiliations

  • Elena A. Ivanova
    • 1
    • 2
  1. 1.Department of Theoretical MechanicsPeter the Great St.Petersburg Polytechnic UniversitySt. PetersburgRussia
  2. 2.Institute for Problems in Mechanical Engineering of Russian Academy of SciencesSt. PetersburgRussia