Active Bound States Arise From Transiently Nonreciprocal Pair Interactions

Static nonreciprocal forces between particles generically drive persistent motion reminiscent of self-propulsion. Here, we demonstrate that reciprocity-breaking fluctuations about a reciprocal mean coupling strength are sufficient to generate this behavior in a minimal two-particle model, with the velocity of the ensuing \textit{active} bound state being modulated in time according to the nature of these fluctuations. To characterize the ensuing nonequilibrium dynamics, we derive exact results for the time-dependent center of mass mean-squared displacement and average rate of entropy production for two simple examples of discrete- and continuous-state fluctuations. We find that the resulting dimer can exhibit unbiased persistent motion akin to that of an active particle, leading to a significantly enhanced effective diffusivity.