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  • Letter

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

M. Baldovin, L. Caprini, and A. Vulpiani
Phys. Rev. E 104, L032101 – Published 7 September 2021
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Abstract

We introduce a general formulation of the fluctuation-dissipation relations (FDRs) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require 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 nonlinear 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.

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  • Figure
  • Received 26 May 2021
  • Accepted 17 July 2021

DOI:https://doi.org/10.1103/PhysRevE.104.L032101

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

M. Baldovin1, L. Caprini2,*, and A. Vulpiani1

  • 1Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy
  • 2Scuola di Scienze e Tecnologie, Università di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy

  • *Corresponding author: lorenzo.caprini@gssi.it

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Issue

Vol. 104, Iss. 3 — September 2021

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