A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining

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

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3 Citations (Scopus)


For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green-Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction A â BA\rightleftarrows B. Furthermore, we show that, for such a system, one cannot find a consistent constitutive law by any Green-Kubo-like scheme.

Original languageEnglish
Pages (from-to)15-33
Number of pages19
JournalJournal of Non-Equilibrium Thermodynamics
Issue number1
Early online date7 Oct 2020
Publication statusPublished - 1 Jan 2021


  • chemical kinetics
  • dissipation
  • fluctuations
  • gradient flows
  • Markov processes


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