Universal Relation between Entropy and Kinetics

Thermodynamic and kinetic properties of materials are usually thought of as unconnected. Relating them is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating entropy and diffusion coefficients. It is universal and applicable to equilibrium as well as nonequilibrium steady states. The relation can be used to obtain useful bounds for the diffusion coefficient (normal or anomalous) from the calculated thermodynamic entropy or, conversely, to estimate the entropy based on measured diffusion coefficients. We demonstrate the validity and usefulness of the relation through several examples. We discuss its broad range of applications, in particular, for nonequilibrium systems.