A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations

Hans Christian Öttinger, Mark A. Peletier, Alberto Montefusco (Corresponding author)

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3 Citations (Scopus)


Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green-Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalJournal of Non-Equilibrium Thermodynamics
Issue number1
Early online date3 Sep 2020
Publication statusPublished - 1 Jan 2021


  • coarse-graining
  • dissipation
  • fluctuations
  • Markov processes


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