Taming Chaos by Understanding its Attraction—Guided Monte Carlo Algorithm for Exploring Basins of Attractions

Legend has it that John von Neumann convinced Claude Shannon to name the average level of surprise (or uncertainty) of a random variable "entropy" because "nobody knows what entropy really is, so in a debate you will always have the advantage." This talk aims to demystify "what entropy really is" by presenting advancements in the basin-volume method for measuring the configurational entropy of generic nonequilibrium processes. Here, the outcomes of the random variable are the stable structures in the system's dynamics, and their probabilities are given by the size of the corresponding basins of attraction. The intractable problem of counting such stable structures is replaced by a tractable sampling problem. We will discuss challenges in this sampling approach and introduce a promising solution: a guided non-reversible Monte-Carlo algorithm that explores the basins of attraction efficiently. Additionally, we will preview exciting applications that ultimately aim to answer the intriguing question: "How many materials exist?"