Unified Linear Fluctuation-Response Theory Arbitrarily Far from Equilibrium

Abstract

Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for near-equilibrium systems, and various bounds have recently been reported for specific non-equilibrium regimes. Here, we present an exact response equality for arbitrary Markov processes that decompose system response into spatial correlations of local dynamical events. This decomposition reveals that response properties are encoded in correlations between transitions and dwelling times across the network, providing a natural generalization of the fluctuation-dissipation theorem and recently developed non-equilibrium linear response relations. Our theory unifies existing response bounds, extends them to time-dependent processes, and reveals fundamental monotonicity properties of the tightness of multi-parameter response inequalities. Beyond its theoretical significance, this framework enables efficient numerical evaluation of response properties from sampling unperturbed trajectories, offering significant advantages over traditional finite-difference approaches for estimating response properties of complex networks and biological systems far from equilibrium.

References in corpus (28)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Mechanics and Statistics of Active Matter
• The large deviation approach to statistical mechanics
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Macroscopic fluctuation theory
• Active matter
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• Accuracy of direct gradient sensing by single cells
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
• An update on nonequilibrium linear response
• Multidimensional thermodynamic uncertainty relations
• Frenesy: time-symmetric dynamical activity in nonequilibria
• Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions
• The Local and the Occupation Time of a Particle Diffusing in a Random Medium
• Limits of sensing temporal concentration changes by single cells
• Response theory: a trajectory-based approach
• Potential and Flux Decomposition for Dynamical Systems and Non-Equilibrium Thermodynamics: Curvature, Gauge Field and Generalized Fluctuation-Dissipation Theorem
• Universal thermodynamic bounds on nonequilibrium response with biochemical applications
• Fundamental Limits on Sensing Chemical Concentrations with Linear Biochemical Networks
• Manifestations of Projection-Induced Memory: General Theory and the Tilted Single File
• Violation of Local Detailed Balance Despite a Clear Time-Scale Separation
• Nonequilibrium Fluctuation-Response Relations: From Identities to Bounds
• Dissipation bounds precision of current response to kinetic perturbations
• Universal energy-accuracy tradeoffs in nonequilibrium cellular sensing
• Dynamical activity universally bounds precision of response in Markovian nonequilibrium systems
• Universal Response Inequalities Beyond Steady States via Trajectory Information Geometry
• Universal Quantum Fluctuation-Dissipation Relation for Systems Far From Equilibrium

Cited by in corpus (4)

• Nonequilibrium fluctuation-response relations for state-current correlations
• Nonequilibrium fluctuation-response relations for state observables
• Macroscopic fluctuation-response theory and its use for gene regulatory networks
• Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems