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The imaginary-time path integral representation of the canonical partitionfunction of a quantum system and non-equilibrium work fluctuation relations arecombined to yield methods for computing free energy differences in quantumsystems using non-equilibrium processes. The path integral representation isisomorphic to the configurational partition function of a classical fieldtheory, to which a natural but fictitious Hamiltonian dynamics is associated.It is shown that if this system is prepared in an equilibrium state, afterwhich a control parameter in the fictitious Hamiltonian is changed in a finitetime, then formally the Jarzynski non-equilibrium work relation and the Crooksfluctuation relation are shown to hold, where work is defined as the change inthe energy as given by the fictitious Hamiltonian. Since the energy divergesfor the classical field theory in canonical equilibrium, two regularizationmethods are introduced which limit the number of degrees of freedom to befinite. The numerical applicability of the methods is demonstrated for aquartic double-well potential with varying asymmetry. A general parameter-freesmoothing procedure for the work distribution functions is useful in thiscontext.

Quantum free energy differences from non-equilibrium path integrals: I. Methods and numerical application