Geometric quantum thermodynamic engine under an isothermal operation: an application of a Thouless pumping

Abstract

Abstract We present a geometric formalism for the non-equilibrium thermodynamics of a small system coupled to external isothermal reservoirs as an application of Thouless pumping, where the electro-chemical potentials of the reservoirs and parameters in the system ʟs Hamiltonian are adiabatically controlled. By analyzing the quantum master equation for the Anderson model of a quantum dot under the wide-band approximation, we obtain the work and effective efficiency of the thermodynamic engine as functions of the phase difference between the externally controlled electrochemical potentials after the system reaches a geometric cyclic state. Since the entropy production is negligible in adiabatic operations, the process we consider is reversible, analogous to the Carnot cycle.