Evolution in complex systems: record dynamics in models of spin glasses, superconductors and evolutionary ecology

TL;DR

This paper reviews how record dynamics, characterized by sporadic quakes, explain the slow, non-stationary evolution in models of spin glasses, superconductors, and ecological systems, highlighting the role of log-Poisson statistics in long-term behavior.

Contribution

It introduces record dynamics as a unifying framework to describe non-stationary evolution in diverse complex systems, supported by analysis of quake timing.

Findings

Quakes cause significant changes in system properties.

Log-Poisson statistics effectively model quake occurrence times.

Record dynamics can predict long-term evolution patterns.

Abstract

Recent research on the non-stationary nature of the dynamics of complex systems is reviewed through three specific models. The long time dynamics consists of a slow, decelerating but spasmodic release of generalized intrinsic strain. These events are denoted quakes. Between the quakes weak fluctuations occur but no essential change in properties are induced. The accumulated effect of the quakes, however, is to induce a direct change in the probability density functions characterising the system. We discuss how the log-Poisson statistics of record dynamics may be an effective description of the long time evolution and describe how an analysis of the times at which the quakes occur enables one to check the applicability of record dynamics.