Abstract

Self-organization (SO) is a ubiquitous phenomenon that has focused much attention and research work. However, analyses of such phenomena are often limited to specific systems and dynamics while a general theoretical modelling has been difficult to formulate. The main difference between thermodynamic equilibrium and dynamics-driven self-organized steady states is that entropy is maximized in the former and mimimized in the latter. This suggests that SO is governed by a general principle: it emerges when a minute subset of system configurations are exceptionally stable and long-lived to survive the noise generated by the driving. Guided by this principle, a statistical mechanics-like model is formulated for general SO and its application is illustrated, with explicit derivations for two example systems: self-organized steady states of quasi-statically driven granular systems in two dimensions and crowd laning. In this formalism, maximizing a survivability function of the exceptionally few stable configurations is the equivalent of minimizing the free energy in traditional statistical mechanics. Parallels with equilibrium statistical mechanics provide useful insight, which should assist in modelling SO in general out-of-equilibrium systems. Time permitting, similarities and differences between SO in passive and biological systems will be pointed out, suggesting potential extension to biology, albeit to very simple systems.