The trouble with free energy landscapes

In Kramers’ theory of chemical reaction rates, classical nucleation theory, phase field modeling, and the modeling of biomolecular kinetics, the dynamics of coarse-grained variables is treated as a stochastic process driven by the gradient of a thermodynamic potential. We will discuss how these models can be motivated based on the physics of the underlying microscopic processes. We will show which (often uncontrolled) assumptions need to be made to arrive at stochastic dynamics in a free energy landscape and we will discuss common misperceptions regarding the fluctuation dissipation theorem.