Geometric effect in nonequilibrium quantum thermodynamics

The concept of work is studied in quantum thermodynamics of a system surrounded by an environment and driven by a slowly varying external force. It is found that there appears the gauge theoretical structure in a nonequilibrium quasistationary state generated from the equilibrium state through a positive operator-valued measure (POVM). The thermodynamic work as the flux of the gauge field is considered for a cyclic process in the space of the external-force parameters. In this way, a novel geometric effect in nonequilibrium quantum thermodynamics is predicted. This effect is illustrated by using an example of a spin-1/2 interacting with a slowly rotating external magnetic field.