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Global effective fluctuation-dissipation relation in particle dynamics and Brownian motion

Chiara Pezzotti and Massimiliano Giona*

  • *Contact author: massimiliano.giona@uniroma1.it
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Phys. Rev. Research 8, 033231 – Published 25 August, 2026

DOI: https://doi.org/10.1103/zl8y-r5vx

Abstract

We introduce the concept of a global effective fluctuation-dissipation relation for thermal particle motion in heterogeneous and disordered systems. The relation connects two effective quantities: the diffusivity, determined from the long-time scaling of the particle mean-square displacement at thermal equilibrium, and the effective friction factor, associated with the linear scaling of the particle terminal velocity in the presence of a constant external force with the intensity of the force itself. The global effective fluctuation-dissipation relation is identically fulfilled by hydromechanic models of fluid-particle interactions in heterogeneous media, i.e., whenever the friction factor either is a function of the particle position or represents a stochastic process. Conversely, models in which heterogeneity is described via a potential landscape do not fulfill this property in general but solely in the limit of small external forces or small intensities of the equilibrium potential.

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Phys. Rev. Research 8, 033231– Published 25 August, 2026
  • Received 11 December 2025
  • Accepted 7 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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