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

Abstract: Recent observations of coordinated self-organisation (SO) of stress and structure in granular systems provide insight into the fundamental principle underlying this phenomenon. It is first argued here that SO emerges when a minute subset of configurations are significantly more stable than the rest and therefore survive the noise in the system much longer to be observed. This principle goes deeper than recently proposed energy considerations. Guided by this principle, a statistical mechanics model is formulated then for SO in these systems and its extension to three dimensions is outlined. The principle holds beyond granular systems and the model is extended next to describe emergence of SO in more general systems. The application of the model is illustrated for the specific example of laning. Parallels of the modelling approach to traditional statistical mechanics provide useful insight that should assist in modelling SO in other out-of-equilibrium systems.