Research

 Traditional fluctuation–response relations break down far from equilibrium, leaving few general tools to predict how strongly a system reacts to small changes. In this study, we present a set of mathematical inequalities that connect fluctuations of physical quantities to their response, which remain valid far from equilibrium and encompass established results as limiting cases. Using a method adapted from information theory, we establish bounds that are independent of system-specific details. The framework captures two distinct types of perturbations: those that alter the balance among possible states and those that change how quickly the system reacts, thereby capturing both thermodynamic and kinetic aspects. Extending the theory to quantum systems interacting with their surroundings reveals that quantum fluctuations impose similar constraints. This unified framework is expected to be useful for theoretically understanding transport phenomena in nanoelectronic devices (e.g., quantum dots) and biochemical processes (e.g., proofreading, sensing).

▶ The ratio between the weighted sum of squared response functions and the fluctuations, computed for randomly generated Markov networks, is bounded. This illustrates fluctuation–response inequalities that generally hold in nonequilibrium systems.

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