Entropy production of active Brownian particles in a rough potential: Role of stochastic fluctuation and temporal correlation

The control of active Brownian particles holds significant promises for diverse applications spanning from biology to artificial intelligence. This work focuses on regulating a non-equilibrium transport of active Brownian particles in a rough potential via energy injecting. By employing path integral method, we derive analytical expressions for the classical trajectory, fluctuation factor, and entropy production. The transition probability along the classical trajectory shows that the system evolves from a non-equilibrium state to a new steady state. This transition undergoes two peaks, and is dominated by the fluctuation factor that varies over time with two peaks. The entropy production decreases linearly to zero over time, and the prominent feature of this process is that this linear decrease is interrupted by a sudden increase and a sudden decrease. And after each such sudden change, the linear law can be restored. These two peaks and two interruptions can be interpreted by the temporal correlations of the positions on the trajectory, there being two intensity enhancements in the process of overall decreasing with time in a shifted power law manner. The exact analytical solutions obtained her ein may deepen our understanding of non-equilibrium thermodynamics in active matter systems.