Volume 101, Number 3, February 2013
|Number of page(s)||6|
|Published online||13 February 2013|
Coarse-graining complex dynamics: Continuous Time Random Walks vs. Record Dynamics
FKF, University of Southern Denmark - Campusvej 55, DK5230, Odense M, Denmark, EU
Received: 23 September 2012
Accepted: 21 January 2013
Continuous Time Random Walks (CTRW) are widely used to coarse-grain the evolution of systems jumping from a metastable sub-set of their configuration space, or trap, to another via rare intermittent events. The multi-scaled behavior typical of complex dynamics is provided by a fat-tailed distribution of the waiting time between consecutive jumps. We first argue that CTRW are inadequate to describe macroscopic relaxation processes for three reasons: macroscopic variables are not self-averaging, memory effects require an all-knowing observer, and different mechanisms whereby the jumps affect macroscopic variables all produce identical long-time relaxation behaviors. Hence, CTRW shed no light on the link between microscopic and macroscopic dynamics. We then highlight how a more recent approach, Record Dynamics (RD), provides a viable alternative, based on a very different set of physical ideas: while CTRW make use of a renewal process involving identical traps of infinite size, RD embodies a dynamical entrenchment into a hierarchy of traps which are finite in size and possess different degrees of meta-stability. We show in particular how RD produces the stretched exponential, power-law and logarithmic relaxation behaviors ubiquitous in complex dynamics, together with the sub-diffusive time dependence of the Mean Square Displacement characteristic of single particles moving in a complex environment.
PACS: 02.50.Ey – Stochastic processes / 89.75.Da – Systems obeying scaling laws / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.