Kinetic Fluctuation-Dissipation Relation in collisionless plasmas: a correlated noise source
Abstract
We here focus on small-scale dynamics of collisionless plasmas by employing a generalized kinetic Langevin framework driven by a stochastic time-correlated forcing. Our investigation captures the steady-state Fluctuation-Dissipation Relation (FDR) where the energy injection at low frequencies is due to the time-correlated forcing and the small-scale energy conversion occurs via Landau damping, the latter --though formally reversible-- acting as an effective dissipation mechanism. We analytically extract the resulting asymptotic spectral scalings across multiple physical regimes and characterize the velocity-space cascade by decomposing the plasma distribution function with Hermite polynomials. The framework is then generalized to a multi-scale forcing scenario in which correlation rates are distributed according to a power-law distribution. This extension provides closed-form analytical expressions that may serve to interpret spacecraft in-situ observations. All analytical predictions are successfully validated through direct numerical integrations of the underlying kinetic equations.
Related
- Fluctuation-dissipation relation in branching particle systems
- Generalized fluctuation-dissipation theorem and Einstein relation in rotating equilibrium
- Schrödinger equations and fluctuation theorems for collisionless plasma systems
- Cramer-Rao Inequality Generalizes the Equilibrium Energy Fluctuation-Response Relation to Nonequilibrium Steady States
- Fluctuation-dissipation relations in isotropic turbulence from Kraichnan's fully resolved DIA closure
BibTeX
@misc{moretti2026kinetic,
title = {{Kinetic Fluctuation-Dissipation Relation in collisionless plasmas: a correlated noise source}},
author = {Fabio Moretti and Oreste Pezzi and Simone Benella and Giuseppe Consolini and Andrea Larosa and Fabio Lepreti and Luca Sorriso-Valvo and Francesco Valentini and Vincenzo Carbone},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29709},
eprint = {2610.29709},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29709},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kinetic Fluctuation-Dissipation Relation in collisionless plasmas: a correlated noise source
AU - Fabio Moretti
AU - Oreste Pezzi
AU - Simone Benella
AU - Giuseppe Consolini
AU - Andrea Larosa
AU - Fabio Lepreti
AU - Luca Sorriso-Valvo
AU - Francesco Valentini
AU - Vincenzo Carbone
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29709
UR - https://arxiv.org/abs/2610.29709
AB - We here focus on small-scale dynamics of collisionless plasmas by employing a generalized kinetic Langevin framework driven by a stochastic time-correlated forcing. Our investigation captures the steady-state Fluctuation-Dissipation Relation (FDR) where the energy injection at low frequencies is due to the time-correlated forcing and the small-scale energy conversion occurs via Landau damping, the latter --though formally reversible-- acting as an effective dissipation mechanism. We analytically extract the resulting asymptotic spectral scalings across multiple physical regimes and characterize the velocity-space cascade by decomposing the plasma distribution function with Hermite polynomials. The framework is then generalized to a multi-scale forcing scenario in which correlation rates are distributed according to a power-law distribution. This extension provides closed-form analytical expressions that may serve to interpret spacecraft in-situ observations. All analytical predictions are successfully validated through direct numerical integrations of the underlying kinetic equations.
ER -