Chapter 16 - Kramers theory

Abstract

Kramers developed an important rate theory that spans a number of dynamical regimes Kramers (1940) [1]. At one extreme, Kramers theory describes a quasi-microcanonical dynamics where the rate is limited by slow energy transfer processes that cannot activate reactants nor quench activated products. At the other extreme, Kramers theory describes processes like nucleation and biomolecular conformational transitions where the dynamics resemble overdamped diffusion over a barrier. An intermediate regime of Kramers theory describes trajectories that cross a critical dividing surface and continue along the reaction coordinate to the product state with few barrier recrossings, almost like the dynamics assumed in transition state theory. These qualitative results have been validated in numerous simulations and even in some experiments. In the high friction limit, the Kramers theory is quantitatively correct. In particular, the high friction Kramers theory corroborates Pontryagin's theory of diffusion over barriers Pontryagin et al. (1933) [2], classic theories of nucleation Agarwal and Peters (2014) [3], theories of polymer relaxation dynamics Skinner and Wolynes (1978) [4], and some predictions about protein folding rates Jacob et al. (1999) [5].