Relaxation patterns and semi-Markov dynamics |
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Authors: | Mark M Meerschaert Bruno Toaldo |
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Institution: | 1. Department of Statistics and Probability, Michigan State University, USA;2. Dipartimento di Matematica e Applicazioni “Renato Caccioppoli” — Università degli studi di Napoli “Federico II”, Italy |
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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. |
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Keywords: | Corresponding author 60K15 60J35 34L10 Relaxation Fractional calculus Bernstein function Semi-Markov process Continuous time random walk Semigroup |
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