TY - JOUR A1 - Öttinger, Hans Christian A1 - Montefusco, Alberto A1 - Peletier, Mark A. T1 - A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations T2 - Journal of Non-Equilibrium Thermodynamics N2 - 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. Y1 - 2021 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8019 VL - 46 IS - 1 SP - 1 EP - 13 PB - De Gruyter ER -