Geometric effect and gauge field in nonequilibrium quantum thermostatistics

The concept of work is studied in quantum thermostatistics of a system surrounded by an environment and driven by a slowly varying external force. It is found that there emerges the gauge theoretical structure in a process with a nonequilibrium quasi-stationary state, the field of which is referred to here as the work gauge field. The thermodynamic work as the flux of the work gauge field is considered for a cyclic process in the space of the external-force parameters. As an example, the system of a spin-1/2 interacting with an external magnetic field is analyzed.