Relaxation patterns and semi-Markov dynamics

By Mark M. Meerschaert, Bruno Toaldo. Stochastic Processes and their Applications, 2015

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Abstract Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variety of relaxation patterns. Power law relaxation is related to fractional derivatives in the time variable. More general relaxation patterns are considered here, and the corresponding semi-Markov processes are studied. Our method, based on Bernstein functions, unifies three different approaches in the literature.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8d9a18569e74da17f95a4703e981386c0d8c9547