Entropy Production of Brownian Macromolecules with Inertia

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such open systems can have a negative entropy production rate and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external forces, which includes a transverse Lorentz force, leading to equilibrium.