Probing rare events in emergent reaction diffusion processes

Chemical and Biological systems utilize complex chemistry to generate patterns and perform computations. Patterns often form away from equilibrium at system sizes where fluctuations are correlated and dominate dynamics, but not yet near the macroscopic limit. This intermediate far from equilibrium regime leads to order and structures not accessible at equilibrium. While we possess a strong understanding of Biological architecture, (eg. at the cellular level) it is the chemistry of reaction-diffusion that ultimately implements and builds order and structure. The lack of synthetic systems that rival biology illustrates how we still have far to go towards understanding emergence of patterns and information processing in reaction-diffusion dynamics. Tensor networks have allowed many-body quantum systems to be studied at system sizes and in detail that exceeds previous methods. In this talk we will show how adapting Tensor networks to classical reaction-diffusion processes yields access to time-dependent joint distributions at system sizes that rival those of kinetic Monte-Carlo schemes such as the Gillespie algorithm but with high fidelity statistics. These statistics will be used to quantify rare events.