First-Passage and Non-Equilibrium Dynamics of Many-Body Systems

Santa Fe Institute, Santa Fe NM

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical and computational research, as well as educational and research training activities, in "non-equilibrium statistical mechanics," the branch of science that describes materials expending energy, changing irreversibly from one form to another, or relaxing toward a final state after being perturbed. Just as static matter has different phases (e.g., water and ice), so dynamical materials also have phases. Part of this project will explore some of these phases. One of the key tools is the first-passage problem, referring to the first time something happens, e.g., a piece of steel fails, in a system buffeted by randomness. First-passage problems abound in condensed-matter and materials physics. In addition to materials failure due to fracture, examples include the motion of polymers on a surface, percolation of chemicals in a porous medium, and the passage of heat or electrical current through a disordered material. The PI and his team will develop new theories to understand complex first-passage phenomena. Concrete applications of first-passage theory to engineering, finance, and biology include predicting failure of an electrical grid, extinction of a bacterial colony, and design of a system to store enough solar power to fulfill the needs of a community through the winter. The PI will analyze available datasets about electrical grid performance and about solar energy fluxes to help formulate and validate the theoretical ideas in non-equilibrium statistical mechanics he develops. Accurate prediction of first-passage probabilities could have policy implications for the use of solar-energy production as materials innovations have driven down the costs. The PI contributes to the educational and training programs at the Santa Fe Institute and is the author of two recent books about first-passage times and their applications. TECHNICAL SUMMARY Equilibrium statistical mechanics is largely understood; on the other hand, there is, so far, no comprehensive theory of materials and phenomena far from equilibrium. This project develops tools and ideas in three related areas of non-equilibrium statistical mechanics relevant to active matter: stochastic ruin problems, exclusion processes, and social dynamics. In stochastic-ruin problems, the goals are to understand how a dynamical process reaches an end state and to optimize stochastic strategies to forestall or promote such end states. These theoretical problems can be framed in terms such as the extinction of a bacterial colony or failure of the power grid. The PI's team will apply extensive experience with first-passage processes to investigate basic questions associated with this theory. The totally asymmetric simple exclusion process (TASEP) has been called the Ising model of non-equilibrium statistical mechanics. Originally introduced to model ribosomal translation, TASEP has also been used to describe vehicular traffic and other examples of active, flowing matter. Just as equilibrium statistical mechanics elucidates the phases of static matter, so TASEP has a rich dynamical phase diagram. This project will investigate TASEP in a junction geometry. The research will determine phases, fluctuations, density profiles, and the presence of shock waves as functions of input and output rates. Social-dynamics models provide a general framework for describing many-body interactions where the interaction topology is more complicated than mean-field or near-neighbor. One application in this project is to the spread of infection during an epidemic, as individuals in a social network adapt by limiting interactions. The PI is co-organizing a conference for November 2020 on "Dynamics of Interacting Contagions." Similar adaptive-network ideas in the form of the ranked-voter model can be applied to the spread of information or misinformation on social media. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.