Molecular motors convert chemical energy into mechanical work while operating in an environment dominated by Brownian motion. The aim of this paper is to explore the flow of energy between the molecular motors and its surroundings, in particular, its
efficiency. Based on the Fokker-Planck equation with either $N$ or infinite chemical states, we find that the energy efficiency of the molecular motors, whether the Stokes efficiency or the usual thermodynamic efficiency, is strictly bounded by 1, because of the dissipation of the energy in both the overdamped surroundings and in the process of the chemical reaction.
In this research, the totally asymmetric exclusion process without particle number conservation is discussed. Based on the mean field approximation and the Rankine-Hugoniot condition, the necessary and sufficient conditions of the existence of the do
main wall have been obtained. Moreover, the properties of the domain wall, including the location and height, have been studied theoretically. All the theoretical results are demonstrated by the computer simulations.
