Topologically-constrained fluctuations and thermodynamics regulate nonequilibrium response

A fruitful technique to infer the physical properties of a system, in and out of equilibrium, is to observe how it responds to external perturbations. Near equilibrium, the Fluctuation-Dissipation Theorem is a powerful tool for rationalizing our observations about response by equating them to fluctuations. Its relevance has driven significant interest in developing similar equalities valid far from equilibrium, leading to critical theoretical insights into the characteristics of nonequilibrium response. Recently a different perspective has been conceptualized, where instead of seeking general fluctuation-response equalities the goal is to identify fundamental limits to nonequilibrium response. Building upon this approach, we prove a novel fluctuation-response inequality and show that an arbitrary nonequilibrium response is constrained by fluctuations of a topological variable and enhanced by nonequilibrium driving. Our fluctuation-response inequality notably requires no kinetic information beyond the state space structure. When applied to models of receptor binding, this prediction reveals that sensitivity is bounded by the steepness of a Hill function with a Hill coefficient enhanced beyond the structural thermodynamic limit by the chemical driving.