Quantum Free Energy Differences from Non-Equilibrium Path Integral Methods*

In this work, we discuss how the imaginary-time path integral representation of the quantum canonical partition function and non-equilibrium work fluctuation relations can be combined to yield methods for computing free energy differences in quantum systems using non-equilibrium processes. The path integral representation is isomorphic to the configurational partition function of a classical field theory to which a natural Hamiltonian dynamics can be associated. It is then shown that both, Jarzynski nonequilibrium work relation and Crooks fluctuation relation, formally hold for this classical field theory. Since the energy diverges in canonical equilibrium, regularization methods need to be introduced in order to limit the number of degrees of freedom M to be finite. The convergence of the work distribution as M tends to infinity is demonstrated analytically for a system composed of a quantum particle trapped in a harmonic well, and numerically for a quartic double-well potential with varying asymmetry. Finally, the method is used to study the relevance of protonic quantum effects in ionic water clusters.