Defining work in quantum mechanics: interfering trajectories and decohering heat baths
The question of how to define the work performed on a quantum system undergoing a thermodynamic process has recently received much attention, particularly in the context of nonequilibrium work relations. For closed quantum systems evolving under time-dependent Hamiltonians, a plausible definition of quantum work is provided by the "two-point measurement" (TPM) protocol, involving projective measurements of the initial and final Hamiltonian. In the first part of my talk, I will show that under this definition the statistical distribution of quantum work values can be understood in terms of classical trajectories that interfere coherently, via path-integral phases, and I will extend this result to describe tunneling into the classically forbidden region.
The second part of the talk concerns the work performed on a quantum system in the presence of a decohering environment, where the system-environment coupling is sufficient to bring about decoherence but too weak to allow for substantial energy exchange between system and environment. I will argue that in this situation the TPM protocol again provides a natural definition of quantum work, and I will show that nonequilibrium work relations remain valid within this scheme.