Stochastic model and optimal controls of an active tracking particle with information processing

Living systems often function with regulatory interactions, but the question of how activity, stochasticity, and regulations work together for achieving different goals still remains puzzling. We propose a stochastic model of an active tracking particle with information processing, where the entropy production and information flow are discussed, with the generalized fluctuation theorem serving as a benchmark for verifying the probability setups. Based on the model, the system performance, in terms of the first passage steps, the total energy consumption, and the thermal efficiency, is analyzed in the variable space of measurement error and control field, leading to discussions on optimal controls of the system. Not only elucidating the basic concepts involved in a stochastic active system with information processing, this prototypical model could also inspire more elaborated modelings of natural smart organisms and industrial designs of controllable active systems with desired physical performances in the future.