We introduce an effective technique for the calculation of the binding free energy in drug-receptor systems using nonequilibrium molecular dynamics and application of the Jarzynski theorem. In essence, this novel methodology constitutes the nonequilibrium adaptation of an ancient free energy perturbation technique called Double Annihilation Method, invented more than 25 years ago [J. Chem. Phys. 1988, 89, 3742-3746] and upon which modern approaches of binding free energy computation in drug-receptor systems are heavily based. The proposed computational approach, termed Fast Switching Double Annihilation Methods (FS-DAM) in honor of its ancient ancestor, is applied to a prototypical example system with multiple binding sites, proving its computational potential and versatility in unraveling multiple site or allosteric binding processes.