Direct measurement of topological barriers governing structural transitions in small colloidal clusters

We use video microscopy to investigate transition kinetics among distinct topological states in four-particle colloidal clusters with short-range interactions. While steady-state distributions are captured solely by net free energy differences, observed transition rates are not. By introducing activation barriers proportional to topological changes between states, we construct a minimal thermodynamic framework that explains both transition rates and equilibrium distributions, with predictive capabilities across a range of interaction strengths. These findings have broad implications for evolutionary dynamics, protein folding, and self-assembly.