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

  • 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.
Author:Hans Christian ÖttingerORCiD, Alberto MontefuscoORCiD, Mark A. PeletierORCiD
Document Type:Article
Parent Title (English):Journal of Non-Equilibrium Thermodynamics
First Page:1
Last Page:13
Publisher:De Gruyter
Year of first publication:2021
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