  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.
