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  • Open Access

Kinetic Energy Diffusivity and Scaling Velocity Correlation Functions

Jing-Dong Bao1,* and Fabio Marchesoni2,3,†

  • *Contact author: jdbao@bnu.edu.cn
  • †Contact author: fabio.marchesoni@pg.infn.it
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Phys. Rev. Lett. 134, 227103 – Published 4 June, 2025

DOI: https://doi.org/10.1103/fmbw-9j8w

Abstract

We propose a Green-Kubo-like relation for kinetic energy diffusivity to investigate the interplay between ergodicity and anomalous diffusion. This approach introduces a fluctuation metric for the time-averaged kinetic energy, which holds for scaling velocity correlation functions. We demonstrate that as stationary diffusive systems transition into an effective ergodic phase, their kinetic energy metric converges to a universal law. This finding provides a robust framework for understanding the dynamics of such systems. Applications to protein folding and single-particle tracking illustrate the practical utility of our approach, offering a clear prescription for extracting key physical parameters, such as the friction constant and relaxation time, from finite experimental datasets. Importantly, this method remains effective even when the underlying processes exhibit weak ergodicity breaking or are bounded. Furthermore, we explore the nonergodic transition associated with the aging velocity correlation function observed in granular gases.

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Phys. Rev. Lett. 134, 227103– Published 4 June, 2025
  • Received 28 January 2025
  • Revised 1 April 2025
  • Accepted 19 May 2025
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