Effective entropy production and thermodynamic uncertainty relation of active Brownian particles

Understanding stochastic thermodynamics of the active Brownian particles system has been an important topic in very recent years. However, thermodynamic uncertainty relation (TUR), a general inequality describing how the precision of an arbitrary observable current is constraint by energy dissipation, has not been fully studied for a many-body level. Here, we address such an issue in a general model of an active Brownian particles system by introducing an effective Fokker-Planck equation, which allows us to identify a generalized entropy production only by tracking the stochastic trajectory of particles' position, wherein an activity and configuration dependent diffusion coefficient come into play an important role. Within this framework, we are able to analyze the entropic bound as well as TUR associated with any generalized currents in the systems. Furthermore, the effective entropy production has been found to be a reliable measure to quantify the dynamical irreversibility, capturing the interface and defects of motility induced phase separation. We expect the new conceptual quantities proposed here to be broadly used in the context of active matter. Published under an exclusive license by AIP Publishing.