Two early stage inverse power-law relaxations in the far from equilibrium dynamics in semi-classical percolative composites

Abstract

In several experiments for measuring various classes of responses, performed at least some four decades ago, on driven physical systems in a far-from-equilibrium (or, from a steady-state) situation, early stage inverse-power-law relaxation dynamics had been observed. Since then, this intriguing behavior raised its head off and on until it regained its central role in the mainstream physical sciences about a decade ago with a breakdown and/or avalanche type (also called self-organized critical) behavior of the sand-pile model and a host of other similar problems. In this communication, we report on the non-equilibrium dynamics in our Random Resistor cum Tunneling-bond Network (RRTN) model. Previously, this semi-classical, or semi-quantum percolative model has been highly successful in explaining the static behavior for various random composite systems. In our dynamic studies for the last several years, we observe two initial power-laws (more than a decade each) and then an exponential relaxation for asymptotically large time scales. Efforts were made to interpret our results with various existing theoretical wisdom/s (which give, only one power-law relaxation for each such system near its breakdown or run-away type state). Obviously, our results (with two different power-laws) are richer than those particular cases. Further, a complete theory is still lacking probably due to a much deeper issue of entropy at stake. The appearance of two power-laws seems to be connected to some non-extensive information-loss / entropy (the experimental systems being mostly athermal) for such systems near their brinks (catastrophic failure not necessarily due to criticality).