Universal Non-equilibrium Response Theory Beyond Steady States

Fluctuation-dissipation relations elucidate the response of near-equilibrium systems to environmental changes, with recent advances extending response theory to non-equilibrium steady states. However, a general response theory for systems evolving far from steady states has remained elusive. Using information geometry of stochastic trajectory probabilities, we derive universal thermodynamic bounds on both linear and nonlinear responses of Markov systems to environmental changes, applicable across all non-equilibrium regimes. This theory establishes a new paradigm in non-equilibrium statistical mechanics, offering a unified perspective on the responsiveness of non-stationary systems to external control and environmental changes. Applicable to systems ranging from biological sensory processes to engineered responsive materials, our framework paves the way for understanding and designing complex responsiveness in far-from-equilibrium stochastic systems.