An update on nonequilibrium linear response

Abstract

The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance, introduces the logarithm of the stationary probability density as observable. The theory of dynamical systems offers an alternative with a formula that continues to work when the stationary distribution is not smooth. We show that this method works equally well for stochastic dynamics, and we illustrate it with a numerical example for the perturbation of circadian cycles. A second "probabilistic" approach starts from dynamical ensembles and expands the probability weights on path space. This line suggests new physical questions, as we meet the frenetic contribution to linear response, and the relevance of the change in dynamical activity in the relaxation to a (new) nonequilibrium condition.

v2: removed typos, updated refs

References in corpus (43)

• Information heat engine: converting information to energy by feedback control
• Steady State Thermodynamics of Langevin Systems
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure
• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• Fluctuations and response of nonequilibrium states
• Equality connecting energy dissipation with violation of fluctuation-response relation
• The effective temperature
• Ageing Properties of Critical Systems
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state
• A review of linear response theory for general differentiable dynamical systems
• Off equilibrium dynamics and aging in unfrustrated systems
• Effective Temperature of Red Blood Cell Membrane Fluctuations
• A fluctuation theorem for currents and non-linear response coefficients
• Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions
• Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function
• A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings
• A far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like model
• Energy dissipation and violation of the fluctuation-response relation in non-equilibrium Langevin systems
• Fluctuation relations in simple examples of non-equilibrium steady states
• Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
• Measuring the fluctuation-dissipation ratio in glassy systems with no perturbing field
• Nonlinear response and fluctuation dissipation relations
• Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics
• The fluctuation-dissipation relation: how does one compare correlation functions and responses?
• A meaningful expansion around detailed balance
• Heat capacity in nonequilibrium steady states
• Time-Reversal and Entropy
• Probing active forces via a fluctuation-dissipation relation: Application to living cells
• The modified Sutherland--Einstein relation for diffusive nonequilibria
• Stochastic perturbations to dynamical systems: a response theory approach
• Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain
• Eulerian and Lagrangian pictures of non-equilibrium diffusions
• An Analytical Construction of the SRB Measures for Baker-type Maps
• Generalized Einstein or Green-Kubo relations for active biomolecular transport
• A field-theoretic approach to nonequilibrium work identities
• Monotone return to steady nonequilibrium
• General properties of response functions of nonequilibrium steady states
• Fluctuation-dissipation relation for chaotic non-Hamiltonian systems
• The fluctuation-dissipation relation in an Ising model without detailed balance
• Universal Properties of Nonlinear Response Functions of Nonequilibrium Steady States
• Static and dynamical nonequilibrium fluctuations

Cited by in corpus (106)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
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• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Time-(ir)reversibility in active matter: from micro to macro
• Unifying Thermodynamic Uncertainty Relations
• Frenesy: time-symmetric dynamical activity in nonequilibria
• Faster uphill relaxation in thermodynamically equidistant temperature quenches
• Odd Diffusivity of Chiral Random Motion
• Frenetic bounds on the entropy production
• Response theory: a trajectory-based approach
• Fluctuation-dissipation relations far from equilibrium
• Nonlinear response of inertial tracers in steady laminar flows: differential and absolute negative mobility
• Linear response theory and Green-Kubo relations for active matter
• The frenetic origin of negative differential response
• On the second fluctuation--dissipation theorem for nonequilibrium baths
• Interacting Brownian dynamics in a nonequilibrium particle bath
• Fluctuation-response relations for nonequilibrium diffusions with memory
• Nonequilibrium fluctuation-dissipation theorem and heat production
• Revising and Extending the Linear Response Theory for Statistical Mechanical Systems: Evaluating Observables as Predictors and Predictands
• Friction and noise for a probe in a nonequilibrium fluid
• On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
• Current fluctuations of interacting active Brownian particles
• Theoretical tools for understanding the climate crisis from Hasselmann's program and beyond
• Macroscopic Stochastic Thermodynamics
• Energetics of active fluctuations in living cells
• Predicting brain evoked response to external stimuli from temporal correlations of spontaneous activity
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Limits of Predictions in Thermodynamic Systems: A Review
• On Some Aspects of the Response to Stochastic and Deterministic Forcings
• Finite-time dynamical phase transition in non-equilibrium relaxation
• Nonequilibrium Response and Frenesy
• Breaking the Fluctuation-Dissipation Relation by Universal Transport Processes
• From Langevin to generalized Langevin equations for the nonequilibrium Rouse model
• Field-dependent ionic conductivities from generalized fluctuation-dissipation relations
• Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect
• Topologically-constrained fluctuations and thermodynamics regulate nonequilibrium response
• Activity driven transport in harmonic chains
• Response Theory and Phase Transitions for the Thermodynamic Limit of Interacting Identical Systems
• Inflow rate, a time-symmetric observable obeying fluctuation relations
• Nonequilibrium temperature response for stochastic overdamped systems
• Linear response in neuronal networks: from neurons dynamics to collective response
• Quadratic response of random and deterministic dynamical systems
• Fluctuations of entropy production of a run-and-tumble particle
• Landau theory for finite-time dynamical phase transitions
• Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks
• A large deviation theory perspective on nanoscale transport phenomena
• Elements of a unified framework for response formulae
• Anomalous force-velocity relation of driven inertial tracers in steady laminar flows
• A general fluctuation-response relation for noise variations and its application to driven hydrodynamic experiments
• Zero-current Nonequilibrium State in Symmetric Exclusion Process with Dichotomous Stochastic Resetting
• Negative Differential Mobility in Interacting Particle Systems
• Quantum response theory for nonequilibrium steady states
• Anomalous mobility of a driven active particle in a steady laminar flow
• Response Formulae for $n$-point Correlations in Statistical Mechanical Systems and Application to a Problem of Coarse Graining
• Nonequilibrium thermodynamics and information theory: Basic concepts and relaxing dynamics
• Linear Stochastic Thermodynamics
• Stochastic thermodynamics of a piezoelectric energy harvester model
• Dispersion for Two Classes of Random Variables: General Theory and Application to Inference of an External Ligand Concentration by a Cell
• Thermodynamic formalism and linear response theory for non-equilibrium steady states
• Thermal response of nonequilibrium RC-circuits
• Time-symmetric current and its fluctuation response relation around nonequilibrium stalling stationary state
• Thermal response in driven diffusive systems
• Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways
• Second Law of Thermodynamics without Einstein Relation
• Thermodynamic constraints on the nonequilibrium response of one-dimensional diffusions
• Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients
• Generalized equipartition for nonlinear multiplicative Langevin dynamics: application to laser-cooled atoms
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• Nonequilibrium corrections to gradient flow
• Midpoint distribution of directed polymers in the stationary regime: exact result through linear response
• Focus on some Nonequilibrium Issues
• Unified Linear Fluctuation-Response Theory Arbitrarily Far from Equilibrium
• Spectroscopy of phase transitions for multiagent systems
• Strong current response to slow modulation: a metabolic case-study
• Understanding Recurrent Neural Networks Using Nonequilibrium Response Theory
• Critical Fluctuations at Finite-Time Dynamical Phase Transition
• Linear response of hydrodynamically-coupled particles under a nonequilibrium reservoir
• The induced friction on a probe moving in a nonequilibrium medium
• Variational time reversal for free energy estimation in nonequilibrium steady states
• Non-equilibrium quantum probing through linear response
• Energy Storage in Steady States under Cyclic Local Energy Input
• Negative response to an excessive bias by a mixed population of voters
• Linear response in the nonequilibrium zero range process
• Violation of the second fluctuation-dissipation relation and entropy production in nonequilibrium medium
• Coupling an elastic string to an active bath: the emergence of inverse damping
• Macroscopic fluctuation-response theory and its use for gene regulatory networks
• Effects from Additional Random Configuration to Linear Response and Modified Fluctuation-Dissipation Relation
• Wasserstein distance in speed limit inequalities for Markov jump processes
• Predictors and Predictands of Linear Response in Spatially Extended Systems
• A General Framework for Linking Free and Forced Fluctuations via Koopmanism
• Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
• Unitary-Scaling Decomposition and Dissipative Behaviour in Finite-Dimensional Linblad Dynamics
• Generalized fluctuation theorems for classical systems
• Nonequilibrium Langevin equation and effective temperature for particle interacting with spatially extended environment
• A Fluctuation-Response Relation as a Probe of Long-Range Correlations in Non-Equilibrium Quantum and Classical Fluids
• Thermal response of a Fermi-Pasta-Ulam chain with Andersen thermostats
• Kolmogorov Modes and Linear Response of Jump-Diffusion Models
• Quantum fluctuation theorem for initial near-equilibrium system
• An expression of excess work during transition between nonequilibrium steady states
• Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response
• Fluctuation-response relation of time-symmetric quantities around general nonequilibrium stationary state
• Divergent stiffness of one-dimensional growing interfaces
• Fluctuation-dissipation supersymmetry
• Fluctuations of driven probes reveal nonequilibrium transitions in complex fluids
• Inducing and optimizing Markovian Mpemba effect with stochastic reset