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- Title
A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations.
- Authors
Öttinger, Hans Christian; Peletier, Mark A.; Montefusco, Alberto
- 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.
- Subjects
NONEQUILIBRIUM statistical mechanics; MARKOV processes; STOCHASTIC differential equations; EVOLUTION equations; JUMP processes
- Publication
Journal of Non-Equilibrium Thermodynamics, 2021, Vol 46, Issue 1, p1
- ISSN
0340-0204
- Publication type
Article
- DOI
10.1515/jnet-2020-0068