The paper by C. Jarzynski explores the relationship between the Helmholtz free energy difference between two equilibrium configurations of a system and the ensemble of finite-time measurements of the work performed when switching an external parameter of the system. The main result established is that the free energy difference can be obtained from the ensemble average of the exponential of the work performed, regardless of the switching time. This is derived within the master equation formalism, which treats the system's evolution as a Markov process satisfying detailed balance. The paper discusses specific examples of stochastic processes that satisfy these conditions, including Hamiltonian evolution, Langevin evolution, isothermal molecular dynamics, and Monte Carlo evolution. It also highlights the potential utility of this result in numerical computations of free energy differences, particularly in methods like thermodynamic integration and thermodynamic perturbation. The key finding is that the exponential average of the work performed over an ensemble of finite-time simulations provides an unbiased estimate of the free energy difference, even though the ordinary average of the work may be biased.The paper by C. Jarzynski explores the relationship between the Helmholtz free energy difference between two equilibrium configurations of a system and the ensemble of finite-time measurements of the work performed when switching an external parameter of the system. The main result established is that the free energy difference can be obtained from the ensemble average of the exponential of the work performed, regardless of the switching time. This is derived within the master equation formalism, which treats the system's evolution as a Markov process satisfying detailed balance. The paper discusses specific examples of stochastic processes that satisfy these conditions, including Hamiltonian evolution, Langevin evolution, isothermal molecular dynamics, and Monte Carlo evolution. It also highlights the potential utility of this result in numerical computations of free energy differences, particularly in methods like thermodynamic integration and thermodynamic perturbation. The key finding is that the exponential average of the work performed over an ensemble of finite-time simulations provides an unbiased estimate of the free energy difference, even though the ordinary average of the work may be biased.