Finite-Time Driven Two-Level Quantum Carnot Engine: Sequential Multicycle Analysis

Abstract Small-scale (microscopic and nanoscopic) heat engines exhibit significant cycle-to-cycle fluctuations in work and heat due to finite-time interactions that induce partial thermalization (PT); in quantum engines with few degrees of freedom, such fluctuations are further enhanced, necessitating multicycle statistical analysis. Prior work (Quadeer et al. 2021 Phys. Rev. E 103 042141) studied two-level quantum Carnot engines via Monte Carlo simulations under the assumption of strong dephasing, where coherences vanish and the dynamics reduce to level populations (diagonal states), with reset initial states to the same equilibrium state with the hot (cold) bath in each run— a standard approach for single-cycle analysis. We go beyond this single-cycle paradigm by considering sequential multicycle operation, where the final state of each cycle serves as the initial state of the next. We show that the efficiencies exceed those of Quadeer et al., especially at short cycle periods. Simulations reveal that a time-dependent effective temperature $\theta(t)$, defined via level populations, undergoes transient crossings: after adiabatic stages, frozen populations cause $\theta(t)$ to briefly exceed $T_h$ (transient overheating) upon hot-bath contact and drop below $T_c$ (transient overcooling) on cold-bath contact, which enhances the net work and thermodynamic efficiency. Therefore, this study reveals an optimization mechanism for finite-time quantum engines rooted in a transient non-equilibrium thermodynamic effect, and establishes a framework for performance enhancement beyond the single-cycle resetting paradigm.