Joint probability densities of an active particle coupled to two heat reservoirs

Abstract

In this paper, we derive an altered Fokker-Planck equation for an active particle with the harmonic, viscous, and random forces, coupled to two heat reservoirs. We attain the solution for the joint distribution density of our topology, including the center topology, the ring topology, and the chain topology, subject to an exponential correlated Gaussian force. The mean squared displacement and the mean squared velocity behavior as the super-diffusions in $t<<\tau$ and for$\tau =0$, while those have the Gaussian forms in $t>>\tau$and for$\tau =0$, where $\tau$ is the correlation time. We concomitantly calculate and analyze the non-equilibrium characteristics of the kurtosis, the correlation coefficient, and the moment from the derived moment equation.