Universal Law for Diffusion in Continuous Potential Energy Landscapes

Using video microscopy and computer simulations, we study the diffusion dynamics of colloidal particles in continuous potential energy landscapes at quasi-two-dimensions. The potential energy landscapes are constructed using scanning optical tweezers in the experiments, and the diffusion coefficients are extracted from the long-time mean squared displacements of tracer particles. We discover a universal relation that quantitatively determines the normalized long-time diffusion coefficient of a colloidal particle from the shape of the potential energy landscape, characterized by the Shannon information entropy S_{N} and a generalized packing fraction ϕ. This relation is validated in a wide range of potential distributions, and over a large dynamic range. As all elemental diffusions can be considered as a dynamical process of exploring an external potential energy landscape by a diffusing particle, this universal law, which reduces multidimensional potential distributions to two dimensionless numbers, provides a quantitative tool to study dynamical phenomena in a wide range of complex environments, where general analytical or empirical models are lacking.