Many of the most basic physical properties of a system, such as its viscosity, elasticity, and conductivity, are determined by observing how it responds to small perturbations. For systems near thermodynamic equilibrium, the fluctuation-dissipation theorem is a powerful theoretical and experimental tool that allows us to determine these response properties simply from the observation of spontaneous fluctuations. As many systems are close to equilibrium, the fluctuation-dissipation theorem has found diverse applications in physics, chemistry, and materials science. However, much of the natural world is not in thermodynamic equilibrium, and the fluctuation-dissipation theorem does not directly apply. In this work, we derive simple, universal thermodynamic constraints on how systems respond to perturbations when arbitrarily far from equilibrium, and we show how these constraints apply to biochemical networks.

Our results are a series of equalities and inequalities that constrain nonequilibrium response in terms of the strength of the nonequilibrium driving such as chemical potential differences and temperature gradients. Our work goes beyond prior results, in part because our bounds depend on these experimentally accessible quantities. We illustrate our results by revisiting well-known biochemical examples and showing how our bounds lead to constraints on a cell’s ability to avoid errors in its molecular processes and to sense chemical concentrations accurately.

Our techniques yield general bounds that promise the ability to transcend the structural complexity of realistic biochemical models. They also offer new insight into principles for designing optimally responsive devices and point to the possibility of developing novel experimental methods for measuring response in complex nonequilibrium matter.