Time translation symmetry, ergodicity and entropy dynamics in a time crystal driven by optical interaction forces

Abstract

Nonreciprocal processes are universally present in living systems, and they control social behavior, kinetic asymmetries in chemistry, pattern formation, and phase transitions in active matter out of equilibrium. It was shown recently that light-induced “predator-prey” interactions in an ensemble of pairs of dissimilar nanoscale oscillators can facilitate the transition to the continuous time-crystal state of matter. Here, we experimentally study the dynamics of time-crystal transitions driven by nonreciprocal optical interaction forces. We observe that the breaking of continuous time-translation symmetry and ergodicity and a decrease in entropy characterize such transitions. Intriguingly, such dynamics are also manifested by living matter. We argue that nonreciprocally driven time crystals represent a powerful platform for studying the classical dynamics of many-body systems, including modeling the matter-to-life transition, and present an opportunity to implement all-optical neural networks and reservoir computing architectures.

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