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

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 nonequilibrium regimes, facilitating consistent optimization of diverse thermal devices in practice.