Vector Field Formalism and Analysis for a Class of Thermal Ratchet

In order to understand the basic physics of muscle contraction and molecular motor movement, we develop a conceptual model for nonequilibrium free energy transduction based on a 2-dimensional diiusion in a periodic force eld. It is shown that a nonconservative force is suucient and necessary for a steady-state with circular ux, but is not suucient for a global uni-directional transport thermal ratchet synonymous to motor protein movement. A vector potential for the ux is introduced for characterizing the circular ux and global transport. The model provides a natural distinction between the two types of models for muscle protein movement, namely the mechanical dominant power-stroke" model and the Brownian-motion dominant ratchet model.