A handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics

Abstract

We introduce a general formulation of the fluctuation-dissipation relations (FDR) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require the explicit knowledge of the stationary probability density function. Our formula applies to Markov stochastic systems with generic noise distributions: when the noise is additive and Gaussian, the relation reduces to those known in the literature; for multiplicative and non-Gaussian distributions (e.g. Cauchy noise) it provides exact results in agreement with numerical simulations. Our formula allows us to reproduce, in a suitable small-noise limit, the response functions of deterministic, strongly non-linear dynamical models, even in the presence of chaotic behavior: this could have important practical applications in several contexts, including geophysics and climate. As a case of study, we consider the Lorenz '63 model, which is paradigmatic for the chaotic properties of deterministic dynamical systems.

References in corpus (35)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• How far from equilibrium is active matter?
• The Physics of Climate Variability and Climate Change
• Fluctuations and response of nonequilibrium states
• Nonequilibrium glass transitions in driven and active matter
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state
• Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
• Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions
• Predicting Climate Change using Response Theory: Global Averages and Spatial Patterns
• Large times off-equilibrium dynamics of a particle in a random potential
• Fluctuation-Dissipation relations in Driven Granular Gases
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
• Nonlinear response and fluctuation dissipation relations
• Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics
• Response theory: a trajectory-based approach
• Fluctuating motion in an active environment
• Linear response theory and Green-Kubo relations for active matter
• Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems
• Extended Fluctuation-Dissipation Theorem for Soft Matter in Stationary Flow
• Linear response and correlation of a self-propelled particle in the presence of external fields
• Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system
• Linear response, susceptibility and resonances in chaotic toy models
• Evaluating linear response in active systems with no perturbing field
• Beyond Forcing Scenarios: Predicting Climate Change through Response Operators in a Coupled General Circulation Model
• On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
• Understanding causation via correlations and linear response theory
• Nonequilibrium Brownian motion beyond the effective temperature
• Generalized fluctuation-dissipation relation and effective temperature in off-equilibrium colloids
• Response of active Brownian particles to shear flow
• Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect
• Frequency-dependent fluctuation-dissipation relations in granular gases
• Generalized Fluctuation-Dissipation relations holding in non-equilibrium dynamics
• Multimodal stationary states under Cauchy noise
• Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise

Cited by in corpus (4)

• Extracting causation from millennial-scale climate fluctuations in the last 800 kyr
• Conceptual and practical approaches for investigating irreversible processes
• The Many Faces of Fluctuation-Dissipation Relations Out of Equilibrium
• Non-equilibrium statistical mechanics of the turbulent energy cascade: irreversibility and response functions