Optimizing low-dissipation Carnot-like thermal devices with heat leak

Delimiting the optimal performance bounds of heat engines (HEs), refrigerators (REs), and heat pumps (HPs) is a core thermodynamic challenge. While low-dissipation (LD) models are valuable for this, the impact of heat leak--unavoidable in real systems--are underexplored. In this paper, we present a unified framework for LD Carnot-like (CL) HEs, REs, and HPs with heat leak, deriving new results for efficiency at maximum power and power at maximum efficiency. Using these, we construct the Pareto fronts, which delineate the optimal power-efficiency trade-offs under realistic conditions. We prove that the bounds of power at fixed efficiency and efficiency at fixed power coincide, forming these fronts, and show that they are achieved by optimizing the average entropy production rate, a principle applicable to all CL devices and beyond the LD assumption.