Effect of timescale on energy landscape: Distinction between free-energy landscape and potential of mean force

We investigate the effects of the timescale of motion on the shape of energy landscapes. The distinction between the free-energy landscape and the potential of mean force is clarified. The former is related to a thermal equilibrium distribution for chosen coordinates, whereas the latter is determined by the mean force exerted on the coordinates in the equilibrium. It is found that the condition for these two energy landscapes to be the same is the constancy of the mean square velocity with respect to the position coordinate. However, even when the condition holds for the chosen coordinates, as the timescale of observation increases, the averaging effect causes a decrease in the mean square velocity nonuniformly in the configuration space, resulting in a larger distinction between the free-energy landscape and the potential of mean force. The results are expected to provide an important basis for the study of long time scale phenomena in large systems. DOI: 10.1103/PhysRevE.87.030803