 determining the probability distribution (or density) formula_37 of an amount of work formula_38 being exerted by a random system trajectory from formula_9 to formula_11, we can write the above equation in terms of the work distribution functions as follows

Note that for the backward transformation, the work distribution function must be evaluated by taking the work with the opposite sign.The two work distributions for the forward and backward processes cross at formula_42.This phenomenon has been experimentally verified using optical tweezers for the
process of unfolding and refolding of a small RNA hairpin and an RNA three-helix junction.