Derivation of the Invariant Free-Energy Landscape Based on Langevin Dynamics

TL;DR

This paper derives a universal, coordinate-independent free-energy landscape formula based on Langevin dynamics, using only observable quantities from time-series data, enhancing predictive reliability.

Contribution

The authors present a unique FEL formula determined by physical principles that depends solely on measurable data, removing unphysical coordinate dependence.

Findings

The new FEL formula is expressed in terms of probability distribution and diffusion matrix.

It coincides with conventional FEL in special cases.

The formula is shown to be unique and robust.

Abstract

Conventionally defined free-energy landscape (FEL) exhibits unphysical dependence on the choice of reaction coordinates and hence lacks universal predictive ability. We here show that three physically plausible requirements uniquely determine the FEL formula for a given reaction coordinate. Our FEL is expressed solely in terms of quantities obtained through time-series data analysis, namely, the probability distribution and the diffusion matrix. It is free from any unphysical coordinate dependence and coincides with the conventional FEL in special cases. The uniqueness and robustness of the formula strongly suggest that our FEL has universal predictive power.