Unified approach to power-efficiency trade-off relations of generic thermal machines

Abstract

We present a general framework for determining the power-efficiency trade-off relations across arbitrary thermal machines, addressing the lack of unified optimization results stemming from their diverse functionalities (e.g., heat engines, refrigerators, and heat pumps). For time-dependent cycle irreversibility $A(τ)$ following a $τ^{-α}$ power law, where $α$ is an interaction-dependent parameter, we show that engineering the interactions between thermal machines and reservoirs enables control over the trade-off relations, with the efficiency at maximum power approaching Carnot efficiency as $α$ increases. Setting $α=1$ naturally recovers typical low-dissipation regime results. Additionally, we derive the first power-efficiency trade-off for finite-time quantum adiabatic Otto machines with $τ^{-2}$-scaling. This work establishes a unified constraint for thermodynamic cycles across non-equilibrium regimes, facilitating consistent optimization of diverse thermal devices in practice.