Rattling Physics with New Math

If you’ve ever watched a large flock of birds on the wing, moving across the sky like a cloud with various shapes and directional changes appearing from seeming chaos, or the maneuvers of an ant colony forming bridges and rafts to escape floods, you’ve been observing what scientists call self-organization. What may not be as obvious is that self-organization occurs throughout the natural world, including bacterial colonies, protein complexes, and hybrid materials. Understanding and predicting self-organization, especially in systems that are out of equilibrium, like living things, is an enduring goal of statistical physics.

This goal is the motivation behind a recently introduced principle of physics called rattling, which posits that systems with sufficiently “messy” dynamics organize into what researchers refer to as low rattling states. Although the principle has proved accurate for systems of robot swarms, it has been too vague to be more broadly tested, and it has been unclear exactly why it works and to what other systems it should apply.

Dana Randall, a professor in the School of Computer Science, and Jacob Calvert, a postdoctoral fellow at the Institute for Data Engineering and Science, have formulated a theory of rattling that answers these fundamental questions. Their paper, “A Local-Global Principle for Nonequilibrium Steady States,” published last week in Proceedings of the National Academy of Sciences, characterizes how rattling is related to the amount of time that a system spends in a state. Their theory further identifies the classes of systems for which rattling explains self-organization.

When we first heard about rattling from physicists, it was very hard to believe it could be true. Our work grew out of a desire to understand it ourselves. We found that the idea at its core is surprisingly simple and holds even more broadly than the physicists guessed.

Dana Randall  Professor, School of Computer Science & Adjunct Professor, School of Mathematics 
Georgia Institute of Technology 

Beyond its basic scientific importance, the work can be put to immediate use to analyze models of phenomena across scientific domains. Additionally, experimentalists seeking organization within a nonequilibrium system may be able to induce low rattling states to achieve their desired goal. The duo thinks the work will be valuable in designing microparticles, robotic swarms, and new materials. It may also provide new ways to analyze and predict collective behaviors in biological systems at the micro and nanoscale.

The preceding material is based on work supported by the Army Research Office under award ARO MURI Award W911NF-19-1-0233 and by the National Science Foundation under grant CCF-2106687. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsoring agencies.

Jacob Calvert and Dana Randall. A local-global principle for nonequilibrium steady states. Proceedings of the National Academy of Sciences, 121(42):e2411731121, 2024.