Nonequilibrium Response Theory: From Precision Limits to Strong Perturbation

Abstract: Understanding the response of nonequilibrium systems to external perturbations remains a fundamental challenge in statistical physics. Here, we prove a novel universal bound stating that the response precision for state observable is fundamentally constrained to 1/2 under single edge or vertex perturbations, independent of system size. Furthermore, we develop exact relations connecting responses to perturbations of arbitrary strengths, extending nonequilibrium response theory beyond the weak-perturbation regime. Through response equalities, we also provide a novel physical interpretation of response sensitivity and recover bounds previously obtained using graph-theoretical methods and extensive linear algebra. Our results provide a general mathematical framework applicable across diverse nonequilibrium systems and offer design principles for optimal sensing and information processing in biochemical systems.