Entropy Production and Thermodynamic Dynamics in Active and Passive Brownian Systems Driven by Time Dependent Forces and Temperatures

In this work, we examine the impact of time-varying temperature and force on the thermodynamic features of active Brownian motor that moves with velocity against the force as well as passive Brownian motor. By deriving analytical expressions In this work, we examine the impact of time-varying temperature and force on the thermodynamic features of active Brownian motor that moves with velocity against the force as well as passive Brownian motor. By deriving analytical expressions for entropy production and entropy extraction rates, we extend the existing theoretical frameworks by considering a force or temperature that varies exponentially, linearly, and quadratically. By studying the system analytically, we investigate how thermal relaxation, steady-state conditions, and nonlinear dissipation effects are affected over time. We find that the total entropy depends only on temperature and viscous friction if the Brownian particle moves freely, while the entropy production and dissipation rates are strongly influenced by the external force.