Entropy Production and Thermodynamic Dynamics in Active and Passive Brownian Systems Driven by Time-Dependent Forces and Temperatures (Contemporary Mathematics, 2025)
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 v0 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. When a Brownian particle is exposed to periodic forcing, entropy production exhibits oscillatory behavior with monotonic decay, whereas periodic impulsive forces induce discrete spikes followed by relaxation, reflecting intermittent energy injection and dissipation. On the other hand, nonperiodic impulsive forces lead to abrupt entropy surges, followed by gradual stabilization, ensuring long-term equilibration. At the stall force, when f = γv0, all thermodynamic rates-including the entropy production and extraction rates vanishes. We believe that our results have broad implications for the optimization of molecular motors, nanoscale transport, and pulse-driven systems. It also provides insights into the design of bio-inspired nanomachines, thermodynamically controlled microfluidic devices, and artificial nanorobots.
Keywords: entropy production; Brownian systems; time-dependent driving forces