Evidence of entropy cascade in collisionless magnetized plasma turbulence

Kawamori, Eiichirou; Lin, Yu-Ting

doi:10.1038/s42005-022-01115-7

Cited by 2 publications

(1 citation statement)

References 37 publications

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“…While the Vlasov equation predicts p q [f ] to be conserved at the fine-grained level, the corresponding quantity p q [f ] for the coarse-grained distribution function f (x, p) will not necessarily be conserved, at any coarse-graining scale [63]. Additionally, phenomena such as shocks or entropy cascades may lead to collisional anomalies [64][65][66][67]. Particle-in-cell simulations of relativistic turbulence confirm that p q grow at a rate comparable to the average momentum as energy is injected into the system [6], which informs models of nonthermal particle acceleration [26,68].…”

Section: Applicationsmentioning

confidence: 99%

Dimensional measures of generalized entropy

Zhdankin

2023

J. Phys. A: Math. Theor.

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Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond the additive definition pioneered by Boltzmann, Gibbs, and Shannon (applicable to thermodynamic equilibria). For generalized entropies to be applied rigorously to nonequilibrium statistical mechanics, we suggest that there is a need for a physically interpretable (dimensional) framework that can be connected to dynamical processes operating in phase space. In this work, we introduce dimensional measures of entropy that admit arbitrary invertible weight functions (subject to curvature and convergence requirements). These ``dimensional entropies'' have physical dimensions of phase-space volume and represent the extent of level sets of the distribution function. Dimensional entropies with power-law weight functions (related to Renyi and Tsallis entropies) are particularly robust, as they do not require any internal dimensional parameters due to their scale invariance. We also point out the existence of composite entropy measures that can be constructed from functionals of dimensional entropies. We calculate the response of the dimensional entropies to perturbations, showing that for a structured distribution, perturbations have the largest impact on entropies weighted at a similar phase-space scale. This elucidates the link between dynamics (perturbations) and statistics (entropies). Finally, we derive corresponding generalized maximum-entropy distributions. Dimensional entropies may be useful as a diagnostic (for irreversibility) and for theoretical modeling (if the underlying irreversible processes in phase space are understood) in chaotic and complex systems, such as collisionless systems of particles with long-range interactions.

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Section: Applicationsmentioning

confidence: 99%

Dimensional measures of generalized entropy

Zhdankin

2023

J. Phys. A: Math. Theor.

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Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

Nastac,

Ewart,

Sengupta

et al. 2024

Phys. Rev. E

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We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C2∝∫∫dxdv〈f2〉—a quantity that here plays the role of (negative) entropy of the distribution function. We find that C2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C2 to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

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Evidence of entropy cascade in collisionless magnetized plasma turbulence

Cited by 2 publications

References 37 publications

Dimensional measures of generalized entropy

Dimensional measures of generalized entropy

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

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