Relaxation patterns and semi-Markov dynamics

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.

References in corpus (4)

• Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
• Solvable non-Markovian dynamic network
• Lévy mixing related to distributed order calculus, subordinators and slow diffusions
• Completely monotone functions and some classes of fractional evolution equations

Cited by in corpus (10)

• Semi-Markov models and motion in heterogeneous media
• Time-changed fractional Ornstein-Uhlenbeck process
• Heavy-tailed fractional Pearson diffusions
• Non-Local Pearson diffusions
• The Havriliak-Negami and Jurlewicz-Weron-Stanislavsky relaxation models revisited: memory functions based study
• From semi-Markov random evolutions to scattering transport and superdiffusion
• Self-similar Cauchy problems and generalized Mittag-Leffler functions
• Fractional derivative defined by non-singular kernels to capture anomalous relaxation and diffusion
• Non-local logistic equations from the probability viewpoint
• Models of space-time random fields on the sphere