# A Maximum Entropy Principle for inferring the Distribution of 3D Plasmoids

## TL;DR

This paper applies the maximum entropy principle to derive the distribution functions of 3D plasmoids in resistive MHD systems, revealing power-law and exponential behaviors for various physical quantities with minimal parameter dependence.

## Contribution

It introduces a maximum entropy framework for modeling 3D plasmoid distributions, providing analytical power-law and exponential forms for key variables, and compares results with observational data.

## Key findings

- Mass, flux, and helicity distributions follow power laws with exponential cutoffs.
- Velocity distribution is flat at low speeds and follows a power law at high speeds.
- Results are largely independent of free parameters.

## Abstract

The Principle of Maximum Entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced. The analysis is undertaken for the 3D case, with mass, total flux and velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux and helicity exhibit a power-law behavior with exponents of $-4/3$, $-2$, $-3$ and $-2$ respectively for small values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of $v = |{\bf v}|$, is shown to be flat for $v \rightarrow 0$, and becomes a power law with an exponent of $-7/3$ for $v \rightarrow \infty$. Most of these results are nearly independent of the free parameters involved in this specific problem. A preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed.