The paper by Gavin E. Crooks explores the relationship between the free energy difference between two equilibrium ensembles of a system and the ensemble average of the work required to switch between these configurations. The key result, which has been previously shown for non-equilibrium systems, is derived under the assumption that the system's dynamics are Markovian and microscopically reversible. This derivation generalizes several relations commonly used in computer simulations to calculate free energy differences. The equality \( e^{-\beta W} = e^{-\beta \Delta F} \) holds for a finite switching process, where \( W \) is the average work and \( \Delta F \) is the free energy difference. This relation is equivalent to thermodynamic integration in the limit of an infinitely long switching process and to thermodynamic perturbation in the limit of infinitely fast switching. The paper highlights that this equality only requires the initial ensemble to be in equilibrium, reducing systematic errors but increasing statistical errors, which may limit its practical application.The paper by Gavin E. Crooks explores the relationship between the free energy difference between two equilibrium ensembles of a system and the ensemble average of the work required to switch between these configurations. The key result, which has been previously shown for non-equilibrium systems, is derived under the assumption that the system's dynamics are Markovian and microscopically reversible. This derivation generalizes several relations commonly used in computer simulations to calculate free energy differences. The equality \( e^{-\beta W} = e^{-\beta \Delta F} \) holds for a finite switching process, where \( W \) is the average work and \( \Delta F \) is the free energy difference. This relation is equivalent to thermodynamic integration in the limit of an infinitely long switching process and to thermodynamic perturbation in the limit of infinitely fast switching. The paper highlights that this equality only requires the initial ensemble to be in equilibrium, reducing systematic errors but increasing statistical errors, which may limit its practical application.