Nonlinear response and fluctuation-dissipation relations

Lippiello, Eugenio; Corberi, Federico; Sarracino, Alessandro; Zannetti, Marco

doi:10.1103/physreve.78.041120

Cited by 74 publications

(106 citation statements)

References 40 publications

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“…This relation, besides being the basis for the FDT, allows to prove the Green-Kubo relation [54] in the case of homogeneous perturbation (k t = k) of a stationary dynamics. Note that other higher order relations may be derived in the context of the non-linear response theory [61].…”

Section: Response Functionmentioning

confidence: 99%

Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale

2011

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In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.

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Section: Response Functionmentioning

confidence: 99%

Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale

2011

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“…Since C is univocally determined by N D , computing D C simply amounts to determine the average time needed for a faceted domain of N D spins to disappear with zero temperature dynamics, namely D C = −8 τ ND /N . In [35] …”

Section: Appendix IImentioning

confidence: 99%

Fluctuations and effective temperatures in coarsening

Corberi

Cugliandolo

2009

J. Stat. Mech.

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We study dynamic fluctuations in non-disordered finite dimensional ferromagnetic systems quenched to the critical point and the low-temperature phase. We investigate the fluctuations of two two-time quantities, called χ and C, the averages of which yield the self linear response and correlation function. We introduce a restricted average of the χ's, summing over all configurations with a given value of C. We find that the restricted average χ C obeys a scaling form, and that the slope of the scaling function approaches the universal value X∞ of the limiting effective temperature in the long-time limit and for C → 0. Our results tend to confirm the expectation that time-reparametrization invariance is not realized in coarsening systems at criticality. Finally, we discuss possible experimental tests of our proposal.

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“…(12)]. We obtain this quantity using the generalization to non-equilibrium states of the fluctuation-dissipation theorem derived in [8,16]. Similarly to the well known equilibrium theorem, this amounts to an analytical relation between χ and certain correlation functions of the unperturbed system, namely the one where the perturbation h is absent.…”

Section: The Ising Model and The Observable Quantitiesmentioning

confidence: 99%

Role of initial state and final quench temperature on aging properties in phase-ordering kinetics

Corberi

Villavicencio-Sanchez

2016

Phys. Rev. E

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We study numerically the two-dimensional Ising model with non-conserved dynamics quenched from an initial equilibrium state at the temperature Ti ≥ Tc to a final temperature T f below the critical one. By considering processes initiating both from a disordered state at infinite temperature Ti = ∞ and from the critical configurations at Ti = Tc and spanning the range of final temperatures T f ∈ [0, Tc[ we elucidate the role played by Ti and T f on the aging properties and, in particular, on the behavior of the autocorrelation C and of the integrated response function χ. Our results show that for any choice of T f , while the autocorrelation function exponent λC takes a markedly different value for Ti = ∞ [λC (Ti = ∞) 5/4] or Ti = Tc [λC (Ti = Tc) 1/8] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing T f is considered, although this is expected to play no role in the large-scale/long-time properties of the system, we show important effects on the quantitative behavior of χ. In particular, data for quenches to T f = 0 are consistent with a value of the response function exponent λχ = 1 2 λC (Ti = ∞) = 5/8 different from the one [λχ ∈ (0.5 − 0.56)] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important pre-asymptotic corrections associated to T f > 0.

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Nonlinear response and fluctuation-dissipation relations

Cited by 74 publications

References 40 publications

Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale

Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale

Fluctuations and effective temperatures in coarsening

Role of initial state and final quench temperature on aging properties in phase-ordering kinetics

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