ARC Colloquium - Jacob Calvert

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Title

A Markov chain theory of nonequilibrium self-organization

Abstract
For matter in thermal equilibrium, like crystalline solids, the Boltzmann-Gibbs distribution explains that ordered configurations are favored because they have lower energy. There is no analogous theory of self-organization for nonequilbirium systems, despite their abundance in nature and importance to science. Recently, Chvykov et al. (Science, 2021) proposed that a property of physical configurations called “rattling” plays a role in nonequilibrium systems analogous to the one that energy plays in equilibrium. The striking accuracy of this prediction has been demonstrated in a variety of experiments, simulations, and numerical studies, but the precise scope of their theory has been unclear, and its mathematical justification has been lacking.

I will identify the hidden assumptions of this theory and provide an exceedingly simple explanation for its success, by translating its main claims into analogous statements about Markov chains. This explanation, in turn, suggests a vast generalization of the Chvykov et al. theory, which I will demonstrate through familiar examples, like dynamics on spin systems. I will discuss applications of our results to the sampling of nonequilibrium steady states; the testing of nonequilibrium thermodynamic principles; and, more broadly, the characterization of the relationship between the local and global “parts” of Markov chains. (Joint work with Dana Randall.)

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ARC Colloquium - Jacob Calvert

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