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 $A\left(\tau \right)$ following a ${\tau }^{-\alpha }$ power law, where $\alpha$ 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 $\alpha$ increases. Setting $\alpha =1$ naturally recovers typical low-dissipation regime results. Additionally, we derive the first power-efficiency trade-off for finite-time quantum adiabatic Otto machines with ${\tau }^{-2}$-scaling. This work establishes a unified constraint for thermodynamic cycles across nonequilibrium regimes, facilitating consistent optimization of diverse thermal devices in practice.

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• Irreversible processes
• Nonequilibrium & irreversible thermodynamics
• Nonequilibrium statistical mechanics
• Efficiency at maximum power
• Heat engines
• Quantum heat engines & refrigerators
• Linear response theory