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

Abstract

Geometric pumping in open quantum systems is commonly described in terms of the Berry--Sinitsyn--Nemenman (BSN) curvature, which determines the geometric contribution to transported quantities under cyclic parameter modulation. In this work, we show that a cyclically driven open quantum system can operate as an isothermal engine through a mechanism that is fundamentally distinct from curvature-driven pumping. In the adiabatic limit, the instantaneous pumping current vanishes, yet a finite work per cycle survives. We demonstrate that this work originates from the parametric dependence of the instantaneous steady state rather than from the BSN curvature. Using a general superoperator formulation, we derive the non-adiabatic expansion of the density matrix and separate reversible and irreversible contributions to work, heat, and entropy production. The entropy production per cycle scales linearly with the operation speed, ensuring reversibility in the strict adiabatic limit. Finite-speed corrections are expressed in terms of a thermodynamic metric defined on the steady-state manifold, leading to a geometric bound on efficiency degradation. As a concrete example, we apply the theory to the Anderson impurity model under cyclic modulation of electrochemical potentials and the strength of Coulomb interaction. In the sequential-tunneling regime, we obtain finite work in the non-adiabatic regime and confirm that finite work persists in the adiabatic limit. These results clarify the geometric structure underlying isothermal cyclic thermodynamics and reveal a class of reversible steady-state engines whose operation is controlled by the geometry of the steady-state manifold rather than by the BSN curvature.