Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Continuum Mechanics with Spontaneous Violations of the Second Law of Thermodynamics

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



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.


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,...

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


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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