Semiclassical work and quantum work identities in Weyl representation

Abstract

We derive a semiclassical nonequilibrium work identity by applying the Wigner–Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us to extend the concept of work to the leading order in ℏ. We propose a geometric interpretation of this semiclassical Jarzynski relation in terms of trajectories in a complex phase space and illustrate it with the exactly solvable case of the quantum harmonic oscillator.