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arXiv · 2004.09120

A framework of nonequilibrium statistical mechanics. I. Role and type of fluctuations

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

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.

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Hans Christian Öttinger, Mark A. Peletier, Alberto Montefusco. 2020-04-20. A framework of nonequilibrium statistical mechanics. I. Role and type of fluctuations. https://doi.org/10.1515/jnet-2020-0068

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