Non-Markovian dynamics of self-propelled active particles

Active matter systems composed of self-propelled particles (SPPs) provide a rich platform for studying emergent behavior far from equilibrium. These particles continuously absorb energy from their surroundings and convert it into directed motion through phoretic mechanisms, generating and responding to self-induced field gradients. We investigate the dynamics of isotropic active particles, such as self-propelled droplets, to uncover general principles of autonomous motion relevant to both biological and synthetic systems. The feedback between particle motion and evolving field trails introduces a form of memory, leading to inherently non-Markovian dynamics. Using a combination of theoretical analysis and numerical simulations, we examine how confinement and interparticle interactions shape SPP behavior. We find a phase transition from static to dynamic motion as phoretic mobility exceeds a critical threshold. For single particles, the dynamics converge on steady oscillations, while few-particle systems exhibit diverse synchronized states. These results highlight how even minimal active systems can generate complex collective dynamics.