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arXiv · 2004.09121

A framework of nonequilibrium statistical mechanics. II. Coarse-graining

Alberto Montefusco·Mark A. Peletier·Hans Christian Öttinger
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Abstract

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 $A \rightleftarrows B$. Furthermore, we show that one cannot find a consistent constitutive law by any Green-Kubo-like scheme.

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Alberto Montefusco, Mark A. Peletier, Hans Christian Öttinger. 2020-04-20. A framework of nonequilibrium statistical mechanics. II. Coarse-graining. https://doi.org/10.1515/jnet-2020-0069

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