Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain

Abstract

In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying markovian dynamics. We show that the method to derive modified fluctuation-dissipation theorems near non-equilibrium stationary states used by J. Prost et al., PRL 103, 090601 (2009), is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano-Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy, in a way which is similar to what has been done recently in the case of MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a brownian particle in an harmonic trap submitted to a quench of temperature and to a time-dependent stiffness. The second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics.

25 pages, 4 figures

References in corpus (8)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Fluctuations and response of nonequilibrium states
• The Einstein relation generalized to non-equilibrium
• Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
• Fluctuation relations in simple examples of non-equilibrium steady states
• Comparison of work fluctuation relations
• General Solutions for Multispin Two-Time Correlation and Response Functions in the Glauber-Ising Chain
• Dynamic Heterogeneity in the Glauber-Ising chain

Cited by in corpus (30)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• An update on nonequilibrium linear response
• Kinetic uncertainty relation
• Frenesy: time-symmetric dynamical activity in nonequilibria
• Response theory: a trajectory-based approach
• Fluctuation-dissipation relations far from equilibrium
• On the "generalized Generalized Langevin Equation"
• Work statistics in stochastically driven systems
• Joint probability distributions and fluctuation theorems
• Periodically driven jump processes conditioned on large deviations
• Nonequilibrium temperature response for stochastic overdamped systems
• Infinite family of second-law-like inequalities
• Fluctuation theorems and inequalities generalizing the second law of thermodynamics off equilibrium
• Fluctuation-dissipation theorem for non-equilibrium quantum systems
• Inequalities generalizing the second law of thermodynamics for transitions between non-stationary states
• Non-adiabatic entropy production for non-Markov dynamics
• Nonequilibrium thermodynamic potentials for continuous-time Markov chains
• Stochastic energetics of a colloidal particle trapped in a viscoelastic bath
• Thermal response of nonequilibrium RC-circuits
• Thermodynamic inference based on coarse-grained data or noisy measurements
• Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients
• Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model
• Prediction of heart rate response to conclusion of spontaneous breathing trial by fluctuation dissipation theory
• Stochastic thermodynamics of a tagged particle within a harmonic chain
• Thermal Contact I : Symmetries ruled by Exchange Entropy Variations
• Effects from Additional Random Configuration to Linear Response and Modified Fluctuation-Dissipation Relation
• A parity breaking Ising chain Hamiltonian as a Brownian motor
• Generalization of Fluctuation-Dissipation Theorem to Systems with Absorbing States
• On the transient Fluctuation Dissipation Theorem after a quench at a critical point
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain