A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations
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Date
2021-01-26
Publication Type
Journal Article
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yes
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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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published
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Journal / series
Volume
46 (1)
Pages / Article No.
1 - 13
Publisher
De Gruyter
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Software
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Subject
Fluctuations; dissipation; Markov processes; Generic; coarse-graining
Organisational unit
03359 - Oettinger, Christian (emeritus) / Oettinger, Christian (emeritus)