  Inspired by the recent development on calculating the free energy change via
a relaxation process [Nat. Phys. 14, 842 (2018)], we investigate the role of
heat released in an irreversible relaxation following a large perturbation.
Utilizing a derivation without microscopic reversibility, we arrive at a new
free energy estimator that employs a volume term to account for missing
important rare events. Applications to harmonic oscillators and particle
insertion in Lennard-Jones fluid agree well with the (numerical) exact
solutions. Our study hence suggests an alternative interpretation to the
insufficient sampling problem in free energy calculations.
