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By integrating 4 lines of thoughts: symmetry breaking originally advanced byAnderson, bifurcation from nonlinear dynamics, Landau's theory of phasetransition, and the mechanism of emergent rare events studied by Kramers, weintroduce a possible framework for understanding mesoscopic dynamics that links(i) fast lower level microscopic motions, (ii) movements within each basin atthe mid-level, and (iii) higher-level rare transitions between neighboringbasins, which have rates that decrease exponentially with the size of thesystem. In this mesoscopic framework, multiple attractors arise as emergentproperties of the nonlinear systems. The interplay between the stochasticityand nonlinearity leads to successive jump-like transitions among differentbasins. We argue each transition is a dynamic symmetry breaking, with thepotential of exhibiting Thom-Zeeman catastrophe as well as phase transitionwith the breakdown of ergodicity (e.g., cell differentiation). The slow-timedynamics of the nonlinear mesoscopic system is not deterministic, rather it isa discrete stochastic jump process. The existence of these discrete states andthe Markov transitions among them are both emergent phenomena. This emergentstochastic jump dynamics then serves as the stochastic element for thenonlinear dynamics of a higher level aggregates on an even larger spatial andslower time scales (e.g., evolution). This description captures thehierarchical structure outlined by Anderson and illustrates two distinct typesof limit of a mesoscopic dynamics: A long-time ensemble thermodynamics in termsof time $t$ tending infinity followed by the size of the system $N$ tendinginfinity, and a short-time trajectory steady state with $N$ tending infinityfollowed by $t$ tending infinity. With these limits, symmetry breaking and cuspcatastrophe are two perspectives of the same mesoscopic system on differenttime scales.

A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales