Motor protein with nonequilibrium potential: Its thermodynamics and efficiency

A nonequilibrium potential function is introduced for a motor protein modeled by a rectified Brownian motion. This result provides a concrete case for a class of nonequilibrium systems in steady state with dissipation which possess a potential function. The potential mu is a natural generalization of the chemical potential for isothermal chemical species and mu=const if and only if the system is in an equilibrium. The steady-state flux Jproportional to-delmu, and the total heat dissipation h(d) equals a surface integral integralmuJ.dS, representing the energy input. In terms of mu and h(d) the thermodynamic energy conservation in the mesoscopic stochastic system can be rigorously established and various types of motor efficiency are elucidated.