Work fluctuations in a generalized Gaussian active bath

Abstract

We theoretically investigate the dynamics and work distribution of a Brownian particle in a Gaussian active bath. By modeling the active noise as a generalized form of Ornstein–Uhlenbeck process (OUP), we show that the dynamics approaches asymptotically to a superdiffusive regime. Two protocols are considered to perform work on the system, and exact expressions for the probability distribution function (PDF) of work are obtained. Further, we show, by employing the large deviation principle (LDP), that the PDF follows an anomalous scaling with time, in contrast to the normal LDP. Then, fluctuation relations (FR) of work are studied to find that the transient FR does not exist, but a non-conventional FR emerges in the long-time limit. Also, the known results for the usual OUP bath are recovered.