Response theory: a trajectory-based approach

Abstract

We collect recent results on deriving useful response relations also for nonequilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two complementary contributions in the response, one entropic the other frenetic. Under time-reversal invariance of the unperturbed reference process, only the entropic term is present in the response, giving the standard fluctuation-dissipation relations in equilibrium. For nonequilibrium reference ensembles, the frenetic term contributes essentially and is responsible for new phenomena. We discuss modifications in the Sutherland-Einstein relation, the occurence of negative differential mobilities and the saturation of response. We also indicate how the Einstein relation between noise and friction gets violated for probes coupled to a nonequilibrium environment. We end with some discussion on the situation for quantum phenomena, but the bulk of the text concerns classical mesoscopic (open) systems. The choice of many simple examples is trying to make the notes pedagogical, to introduce an important area of research in nonequilibrium statistical mechanics.

References in corpus (87)

• Dynamical ensembles in stationary states
• Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• How far from equilibrium is active matter?
• The Fluctuation Theorem as a Gibbs Property
• Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
• Fluctuations and response of nonequilibrium states
• Equality connecting energy dissipation with violation of fluctuation-response relation
• Odd elasticity
• Odd viscosity in chiral active fluids
• A self-propelled particle in an external potential: is there an effective temperature?
• The effective temperature
• Thermodynamics of Quantum Jump Trajectories
• The statistical physics of active matter: from self-catalytic colloids to living cells
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state
• A review of linear response theory for general differentiable dynamical systems
• Comparison of far-from-equilibrium work relations
• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Non-linear susceptibility in glassy systems: a probe for cooperative dynamical length scales
• Aging, rejuvenation and memory : the example of spin glasses
• An update on nonequilibrium linear response
• Kinetic uncertainty relation
• Frenesy: time-symmetric dynamical activity in nonequilibria
• 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 far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like model
• Fluctuation relations in simple examples of non-equilibrium steady states
• An expression for stationary distribution in nonequilibrium steady state
• Getting More from Pushing Less: Negative Specific Heat and Conductivity in Non-equilibrium Steady States
• Measuring the fluctuation-dissipation ratio in glassy systems with no perturbing field
• From single-particle to collective effective temperatures in an active fluid of self-propelled particles
• Nonlinear response and fluctuation dissipation relations
• Microscopic theory for negative differential mobility in crowded environments
• Active processes in one dimension
• Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics
• Nonlinear response of inertial tracers in steady laminar flows: differential and absolute negative mobility
• Fluctuation-dissipation relations far from equilibrium
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• The adiabatic theorem and linear response theory for extended quantum systems
• Time-symmetric fluctuations in nonequilibrium systems
• A meaningful expansion around detailed balance
• The frenetic origin of negative differential response
• 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
• Time reversal symmetry breaking and odd viscosity in active fluids: Green-Kubo and NEMD results
• On the second fluctuation--dissipation theorem for nonequilibrium baths
• Frenetic aspects of second order response
• Nonlinear Response With Dichotomous Noise
• Probing active forces via a fluctuation-dissipation relation: Application to living cells
• Fluctuation-response relations for nonequilibrium diffusions with memory
• Friction and noise for a probe in a nonequilibrium fluid
• On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
• The modified Sutherland--Einstein relation for diffusive nonequilibria
• Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain
• The modified Langevin description for probes in a nonlinear medium
• Negative differential response in chemical reactions
• Fluctuation-dissipation relations and field-free algorithms for the computation of response functions
• Revisiting the Glansdorff-Prigogine criterion for stability within irreversible thermodynamics
• Nonequilibrium Response and Frenesy
• Fluctuations and response in a non-equilibrium micron-sized system
• Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables
• Large Deviations and a Fluctuation Symmetry for Chaotic Homeomorphisms
• Nonequilibrium temperature response for stochastic overdamped systems
• Jumptime unraveling of Markovian open quantum systems
• The induced motion of a probe coupled to a bath with random resettings
• 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
• Second law of thermodynamics for macroscopic mechanics coupled to thermodynamic degrees of freedom
• Semi-classical approximations based on Bohmian mechanics
• Brownian motion at absolute zero
• A fluctuation-response relation of many Brownian particles under non-equilibrium conditions
• Thermal response of nonequilibrium RC-circuits
• Temperature response in nonequilibrium stochastic systems
• Thermoelectric phenomena via an interacting particle system
• Thermal response in driven diffusive systems
• Measurement of second-order response without perturbation
• On a response formula and its interpretation
• From dynamical systems to statistical mechanics: the case of the fluctuation theorem
• Extrapolation to nonequilibrium from coarse grained response theory
• Nonequilibrium corrections to gradient flow
• Two theorems that relate discrete stochastic processes to microscopic mechanics
• Midpoint distribution of directed polymers in the stationary regime: exact result through linear response
• Spin evolution of cold atomic gases in SU(2)$\otimes$U(1) fields
• Linear response in the nonequilibrium zero range process
• Thermal response of a Fermi-Pasta-Ulam chain with Andersen thermostats

Cited by in corpus (44)

• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• Local detailed balance
• Play. Pause. Rewind. Measuring local entropy production and extractable work in active matter
• Fluctuating motion in an active environment
• Active matter under control: Insights from response theory
• On Some Aspects of the Response to Stochastic and Deterministic Forcings
• Activity driven transport in harmonic chains
• Generalized Fluctuation-Dissipation relations holding in non-equilibrium dynamics
• Trees and forests for nonequilibrium purposes: an introduction to graphical representations
• Time-symmetric current and its fluctuation response relation around nonequilibrium stalling stationary state
• Universal Response Inequalities Beyond Steady States via Trajectory Information Geometry
• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Pushing run-and-tumble particles through a rugged channel
• Affine relationships between steady currents
• When does an active bath behave as an equilibrium one?
• The Many Faces of Fluctuation-Dissipation Relations Out of Equilibrium
• Observation of Nonlinear Response and Onsager Regression in a Photon Bose-Einstein Condensate
• Stochastic Distinguishability of Markovian Trajectories
• Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation-Dissipation Inequalities
• Unified Linear Fluctuation-Response Theory Arbitrarily Far from Equilibrium
• Fluctuation Dissipation Relations for Active Field Theories
• A Thermodynamic Non-Linear Response Relation
• Statistical mechanical foundation of Weber-Fechner laws
• Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control
• A handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics
• The induced friction on a probe moving in a nonequilibrium medium
• Nonequilibrium fluctuation-response relations for state-current correlations
• Nonequilibrium fluctuation-response relations for state observables
• Effective Dynamics of Tracer in Active Bath: A Mean-field Theory Study
• Violation of the second fluctuation-dissipation relation and entropy production in nonequilibrium medium
• Macroscopic fluctuation-response theory and its use for gene regulatory networks
• Nonlinear Langevin functionals for a driven probe
• Coupling an elastic string to an active bath: the emergence of inverse damping
• Perturbative expansion of irreversible works in symmetric and asymmetric processes
• Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
• Probing the limits of effective temperature consistency in actively driven systems
• Wasserstein distance in speed limit inequalities for Markov jump processes
• Entropy as Noether charge for quasistatic gradient flow
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Stochastic Two-temperature Nonequilibrium Ising model
• Fluctuation-response theorem for Kullback-Leibler divergences to quantify causation
• A Rayleigh criterion for mechanical instability: inducing activity by chemo-mechanical coupling
• Nonequilibrium statistical mechanics for stationary turbulent dispersion
• Effective diffusion of a tracer in active bath: a path-integral approach