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Jarzynski's identity for the free energy difference between two equilibriumstates can be viewed as a special case of a more general procedure based onphase space mappings. Solving a system's equation of motion by approximatemeans generates a mapping that is perfectly valid for this purpose, regardlessof how closely the solution mimics true time evolution. We exploit this fact,using crudely dynamical trajectories to compute free energy differences thatare in principle exact. Numerical simulations show that Newton's equation canbe discretized to low order over very large time steps (limited only by thecomputer's ability to represent resulting values of dynamical variables)without sacrificing thermodynamic accuracy. For computing the reversible workrequired to move a particle through a dense liquid, these calculations are moreefficient than conventional fast switching simulations by more than an order ofmagnitude. We also explore consequences of the phase space mapping perspectivefor systems at equilibrium, deriving an exact expression for the statistics ofenergy fluctuations in simulated conservative systems

Equilibrium free energies from fast-switching trajectories with large time steps