Self-organisation -- the underlying principle and a general formalism

Abstract

It is proposed that self-organisation (SO) in non-equilibrium systems 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 and environmental constraints. Guided by this principle, a statistical mechanics-like model is formulated for general SO and its application is illustrated for two example systems: self-organised steady states of quasi-statically driven granular systems in two dimensions and crowd laning, for which illustrative explicit results are derived. In this formalism, maximising a survivability function of the exceptionally few stable configurations is the equivalent of minimising the free energy in traditional statistical mechanics. Parallels with equilibrium statistical mechanics and differences from it are discussed, which provides useful insight to assist in modelling SO in general out-of-equilibrium systems. Similarities and differences between SO in passive and biological systems are also pointed out, suggesting potential extension of this approach in this direction, albeit to very simple systems.