Matching correlations matters: Modeling friction in a hydrophobic folding transition

The generalized Langevin equation provides a powerful framework for modeling and interpreting the conformational dynamics of (macro)molecules in solution. However, recent studies have shown that the standard fluctuation-dissipation relation-linking the memory kernel to the statistics of the random force-can include a non-zero cross correlation term between conservative and random forces. This raises questions about how to correctly extract memory kernels from simulation data when this correlation is neglected and whether inverting the Volterra equation to obtain a memory kernel yields a physically meaningful result. In a recent work [Wolf et al. J. Chem. Phys. 162, 054113 (2025)], we proposed an approximation to account for the cross correlation term. We demonstrate in this work that cross correlations play a significant role in the collapse transition of a hydrophobic polymer under various solvent conditions. In addition, we demonstrate that our proposed approximation yields an improved description of barrier crossing times. Notably, we find that this improvement has the same magnitude as the improvement gained by accounting for memory effects.