Universal Thermodynamic Bounds on Nonequilibrium Response with Biochemical Applications

Abstract

Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of response by observing spontaneous equilibrium fluctuations. In this spirit, we derive here a collection of equalities and inequalities valid arbitrarily far from equilibrium that constrain the response of nonequilibrium steady states in terms of the strength of nonequilibrium driving. Our work opens new avenues for characterizing nonequilibrium response. As illustrations, we show how our results rationalize the energetic requirements of common biochemical motifs.

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Plain Language Summary

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.