The adaptive biasing force algorithm with non-conservative forces and related topics

We propose a study of the Adaptive Biasing Force method's robustness under generic (possibly non-conservative) forces. We first ensure the flat histogram property is satisfied in all cases. We then introduce a fixed point problem yielding the existence of a stationary state for both the Adaptive Biasing Force and Projected Adapted Biasing Force algorithms, relying on generic bounds on the invariant probability measures of homogeneous diffusions. Using classical entropy techniques, we prove the exponential convergence of both biasing force and law as time goes to infinity, for both the Adaptive Biasing Force and the Projected Adaptive Biasing Force methods.

Automated summary

The study proposes an investigation into the robustness of the Adaptive Biasing Force method under generic (possibly non-conservative) forces. The researchers ensure the satisfaction of the flat histogram property and establish the existence of a stationary state for both the Adaptive Biasing Force and Projected Adapted Biasing Force algorithms. Using classical entropy techniques, the study proves the exponential convergence of the biasing force and law over time for both methods.