A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining
Alberto Montefusco, Mark A. Peletier, Hans Christian Öttinger
Abstract
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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>A</m:mi> <m:mo>⇄</m:mo> <m:mi>B</m:mi> </m:math> A\rightleftarrows B . Furthermore, we show that, for such a system, one cannot find a consistent constitutive law by any Green–Kubo-like scheme.