Probing subglass relaxation in polymers via a geometric representation of probabilities, observables, and relaxation...

The dynamics of many physical, chemical, and biological systems can be reduced to a succession of infrequent transitions in a network of discrete states representing low energy regions in configuration space. This enables accessing long-time dynamics and predicting macroscopic properties. Here we develop a new, perfectly general statistical mechanical/geometric formulation that expresses both state probabilities and all observables in the same Euclidean space, spanned by the eigenvectors of the symmetrized time evolution operator. Our formalism leads to simple expressions for nonequilibrium and equilibrium ensemble averages, variances, and time correlation functions of any observable and allows a rigorous decomposition of the dynamics into relaxation modes. Applying it to subglass segmental relaxation in atactic polystyrene up to times on the order of 10 micros, we probe the molecular mechanism of the gamma and delta processes and unequivocally identify the delta process with rotation of a single phenyl group around its stem.