Pareto-optimal control strategies in intrinsically nonequilibrium systems

Abstract: Thermodynamic control is typically formulated as the optimisation of a single objective, yet competing costs rarely admit a common optimum, so single-objective control captures only one corner of the achievable performance space. We develop a general framework for multi-objective thermodynamic control of intrinsically nonequilibrium systems that maps out the full Pareto front of optimal control strategies. We show that Pareto-optimal protocols generically consist of smooth branches connected by boundary jumps, and that the relative weights of the objectives combine with the physical parameters into a single intrinsic scale that alone governs the trade-off. Remarkably, this scale plays a double role: it parametrizes a single functional form that generates the entire front, and it defines control equivalence classes, in which systems with different parameters but the same scale share identical optimal strategies. We illustrate the framework for two paradigmatic systems that are experimentally accessible: transport of an active particle in a harmonic trap, and a cyclic quantum-dot engine. For both, we obtain the Pareto front and optimal strategies in closed form.