Thermodynamic description of active brownian particle driven by fractional gaussian noise

Abstract

As a natural extension of the recent results on the thermodynamics of an active Brownian particle (self-propelled), we study the thermodynamics of an active Brownian particle (ABP) driven by fractional Gaussian noise (FGN). To serve as a prelude of the main results, we start from the conventional Markov process but with time dependent diffusion coefficient, where deviation in integral fluctuation relation (IFR) for total entropy production requires a general definition of the temperature, following the same case for a Brownian particle. In other words, the general temperature definition for this case is independent to the statistics of the rotational motion. We then proceed with the main problem of the paper, which is an active Brownian particle driven by fractional Gaussian noise. Under the assumption that self-propulsion is even under time-reversal, temperature is defined as well as the distance on how far the IFR for total entropy production deviates from the standard definition by adopting the standard definition of trajectory-level entropy and the joint probability of ABP. Furthermore, second law-like concept based on the found deviation is derived, as well as a generalized Clausius inequality. Lastly, magnitude of this deviation diminishes in the case of pure white noise.