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

A 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.