Seminar

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Fundamentals of statistical mechanics explain that systems in thermal equilibrium spend a greater fraction of their time in states with apparent order because these states have lower energy. This explanation is remarkable, and powerful, because energy is a "local" property of states. While non-equilibrium systems can similarly exhibit order, there can be no property of states analogous to energy that generally explains why it emerges. However, recent experiments suggest that a local property called “rattling” predicts which states are favored, at least for a broad class of non-equilibrium systems.

In this seminar, I will present a simple Markov chain theory of rattling that explains when and why it works. This theory motivates new questions concerning the complexity of the relationship between a Markov chain's transition rates and its stationary distribution. The underlying principle is that, although the stationary distribution is generally a complicated function of the transition rates, in many cases it is closely approximated by a simple function of the exit rates alone. As one example, I will present recent work which establishes this picture for Markov chains with i.i.d. random directed rates, which are generally non-reversible, under certain tail conditions on the rate distribution. (This talk features joint work with Dana Randall and Frank den Hollander.)