Vector Field Formalism and Analysis for a Class of Thermal Ratchets

To understand the physics of muscle contraction and molecular motor movement, we develop a model for nonequilibrium free energy transduction based on a diffusion in a periodic force field. It is shown that a nonconservative force is sufficient and necessary for a steady state with circular flux, but is not sufficient for a global unidirectional transport synonymous to motor protein movement. A vector potential for the flux is introduced for characterizing the circular flux and global transport. The model provides a natural distinction between the two types of muscle protein movement, namely the mechanical dominant “power-stroke” and the Brownian-motion dominant ratchet.