von Neumann entropy of phase space structures in gyrokinetic plasma turbulence

TL;DR

This paper introduces a data-driven entropy measure based on SVD to analyze phase-space complexity in gyrokinetic turbulence, revealing how kinetic processes vary with wavenumber and providing a new diagnostic tool.

Contribution

It develops a novel von Neumann entropy diagnostic combining SVD and information theory to quantify velocity-space complexity in gyrokinetic turbulence without predefined bases.

Findings

vNE remains low at low wavenumber but increases near $k_ot ho_{ti} \\sim 1$

Finite Larmor radius phase mixing is active in the perpendicular direction

Enhanced parallel phase mixing correlates with increased vNE and Hermite spectrum broadening

Abstract

We introduce a data-driven diagnostic that combines the singular value decomposition (SVD) with an information-theoretic entropy to quantify the phase-space complexity of perturbed distribution functions in gyrokinetic turbulence. Applying this framework to nonlinear flux-tube simulations that solve the time evolution of the ion distribution function represented by Fourier modes with the wavenumber for real space, we define the von Neumann entropy (vNE) to analyze the velocity-space structure. A global survey in the wavenumber space reveals a wavenumber-dependent variation of the vNE in velocity-space structure: the vNE remains low at low wavenumber but increases across $k_\perp\rho_{t\mathrm{i}}\sim 1$. Hermite/Laguerre decompositions revealed that the finite Larmor radius (FLR) phase mixing in the perpendicular (magnetic-moment) direction is active. Simultaneously, the systematic increase in vNE for $k_\perp\rho_{t\mathrm{i}}$ correlates with the broadening of the Hermite spectrum, suggesting enhanced parallel phase mixing (Landau resonance) as the primary mechanism for the observed wave number dependence. These results demonstrate that the SVD-based vNE provides a compact measure of kinetic complexity without assuming a predefined basis and enables a global mapping of its wavenumber dependence of phase-mixing processes in gyrokinetic turbulence.