A Markov Chain Theory of Self-organization

Abastract: Fundamentals of statistical mechanics explain that systems in thermal equilibrium spend more time in states with greater order because these states have lesser energy. This explanation is remarkable, and powerful, because energy is a “local” property of states. Nonequilibrium systems, like living systems, can also exhibit order, but there is no property analogous to energy that generally explains why states with greater order tend to emerge. However, recent experiments suggest that a local property called “rattling” predicts which states are favored, at least for a broad class of nonequilibrium systems. In this seminar, I will present a simple theory of rattling that explains when and why it works, and I will demonstrate its application to systems across scientific domains. Surprisingly, the core idea of rattling is so general as to apply to equilibrium and nonequilibrium systems alike. (Joint work with Dana Randall.)