Entropy Production of Brownian Macromolecules with Inertia

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system 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 force, which includes the transverse Lorentz force, leading to equilibrium.

Figure 1

A schematic diagram of a 3D macromolecule immersed in a water heat bath under a control force $\overrightarrow{g}=-\alpha \overrightarrow{v}$ and frictional force $\overrightarrow{f}=-\gamma \overrightarrow{v}$ with positive $\alpha$, $\gamma$. The second law of thermodynamics and energy conservation require $d{W}_B=d{W}_{\mathrm{R}\mathrm{W}\mathrm{S}}-dQ-d{Q}_R\le d{W}_{\mathrm{R}\mathrm{W}\mathrm{S}}$, where RWS stands for reversible work source.