Markovian description of active particles driven by colored noise

Active 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 modeled 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, various Markovian approximation schemes have been proposed to replace the colored noise with a multiplicative Gaussian white noise; however, these approaches may restore equilibrium-like steady-state behaviors, failing to capture the nonequilibrium aspects of the steady state. We 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.