Abstract

Self-propelled particles form a class of nonequilibrium systems with constant injection of energy on a microscopic scale. Given sufficient time-scale separation, the dynamics of such particles can be modelled as Brownian motion violating the fluctuation-dissipation relation, namely Langevin dynamics with an instantaneous damping force and a Gaussian colored noise with rapidly decaying correlations. To make the model analytically tractable, previous studies have proposed various Markovian approximation schemes which replace the coloured noise with a multiplicative Gaussian white noise; however, these approaches are not systematic and may restore equilibrium-like steady-state behaviours, failing to capture the nonequilibrium aspects of the steady state. In this talk, I present a systematic Markovian approximation, which yields a Langevin equation with a multiplicative non-Gaussian white noise. The nonzero skewness of the noise is shown to be essential for correctly predicting the evolution of the probability distribution function. The approach provides a convenient and reliable method for predicting nonequilibrium currents, forces, and first-passage time statistics associated with self-propelled particles.