Exact moments for trapped active particles: inertial impact on steady-state properties and re-entrance

Abstract

Abstract In this study, we investigate the behavior of inertial active Brownian particles in a d-dimensional harmonic trap in the presence of translational diffusion. While the solution of the Fokker-Planck equation is generally challenging, it can be utilized to compute the exact time evolution of all time- dependent dynamical moments using a Laplace transform approach. We present the explicit form for several moments of position and velocity in d-dimensions. An interplay of time scales assures that the effective diffusivity and steady-state kinetic temperature depend on both inertia and trap strength, unlike passive systems. The distance from equilibrium, measured by the violation of equilibrium fluctuation-dissipation and the amount of entropy production, decreases with increasing inertia and trap strength. We present detailed ‘phase diagrams’ using kurtosis of velocity and position, showing possibilities of re-entrance to equilibrium.