  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.
