Geometric Quantum Thermodynamic Engine under an Isothermal Operation: An Application of a Thouless Pumping

TL;DR

This paper develops a geometric formalism for quantum thermodynamic engines operating under isothermal conditions, utilizing Thouless pumping to analyze work and efficiency in adiabatic quantum systems.

Contribution

It introduces a novel geometric approach to quantum thermodynamics applied to a Thouless pump, linking adiabatic control parameters to engine performance.

Findings

Work and efficiency depend on the phase difference in electrochemical potentials.

The process is effectively reversible with negligible entropy production.

Engine performance can be characterized through geometric cyclic states.

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 electrochemical potentials of the reservoirs and parameters in the system's 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.