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 μ is a natural generalization of the chemical potential for isothermal chemical species and μ=const if and only if the system is in an equilibrium. The steady-state flux J∝-∇μ, and the total heat dissipation h_d equals a surface integral ∫μJ⋅dS, representing the energy input. In terms of μ and h_d the thermodynamic energy conservation in the mesoscopic stochastic system can be rigorously established and various types of motor efficiency are elucidated.