Record dynamics of evolving metastable systems: theory and applications

Abstract

Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the transitions from one stage to the next. This phenomenology is well known in physics as “physical aging”, but from the vantage point of RD, the evolution of a class of systems of physical, biological, and cultural origin is rooted in a hierarchically structured configuration space and can, therefore, be analyzed by similar statistical tools. This colloquium paper strives to present in a coherent fashion methods and ideas that have gradually evolved over time. To this end, it first describes the differences and similarities between RD and two widespread paradigms of complex dynamics, Self-Organized Criticality and Continuous Time Random Walks. It then outlines the Poissonian nature of records events in white noise time-series, and connects it to the statistics of quakes in metastable hierarchical systems, arguing that the relaxation effects of quakes can generally be described by power laws unrelated to criticality. Several different applications of RD have been developed over the years. Some of these are described, showing the basic RD hypothesis and how the log-time homogeneity of quake dynamics, can be empirically verified in a given context. The discussion summarizes the paper and briefly mentions applications not discussed in detail. Finally, the outlook points to possible improvements and to new areas of research where RD could be of use. Graphic Abstract

Human wealth evolution is an accelerating expansion underpinned by a decelerating optimization process

“…The data points from different regions have now similar τ values and the number of quakes grows at a decelerating rate, r q (τ ) ∝ ln(τ ). This behavior is strongly reminiscent of Record Dynamics [13] a description of complex systems, whose evolution through metastable stages is driven by an optimization process.…”

“…Wealth evolution in terms of τ has just two different regimes that both feature logarithmic growth and are connected by a rapid crossover. We find a strong indication that quakes are a log-Poisson [13] process, which is the hallmark of an optimization process. An underlying evolutionary optimization process [1] might therefore drive the evolutionary expansion of the economic wealth development.…”

“…GDP growth now appears as a decelerating optimization dynamics in a metastable complex systems, a type of process described in Record Dynamics (RD) [13]. In essence, RD links a decreasing rate of change of macroscopic variables to a hierarchy of dynamical barriers separating increasingly robust metastable states [13].…”

“…GDP growth now appears as a decelerating optimization dynamics in a metastable complex systems, a type of process described in Record Dynamics (RD) [13]. In essence, RD links a decreasing rate of change of macroscopic variables to a hierarchy of dynamical barriers separating increasingly robust metastable states [13]. Once the effect of the ever increasing interaction intensity is removed by replacing t with τ , the structures regulating human behavior become indeed progressively harder to change.…”

“…Each section is interpreted as a metastable stage of a dynamical process. The transitions from one stage to the next are called 'quakes' [13] and allegedly express important societal transformations and/or historical events.…”