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.
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