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 |
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Document Type: | Article |
Parent Title (English): | Journal of Non-Equilibrium Thermodynamics |
Volume: | 46 |
Issue: | 1 |
First Page: | 1 |
Last Page: | 13 |
Publisher: | De Gruyter |
Year of first publication: | 2021 |
DOI: | https://doi.org/10.1515/jnet-2020-0068 |