Deus Ex Statistica: A Statistical Solution to the binary-binary Outcome of the Chaotic, Non-Hierarchical Four-Body Problem
Abstract
We present an analytical, statistical solution to the binary-binary (2+2) outcome of the chaotic non-hierarchical four-body problem. The solution is based on the density-of-states formulation pioneered by J. J. Monaghan. The method skips the computationally expensive integration of the equations of motion, and instead samples the outcome from the chaotic phase-space, subject to conservation of energy, momentum, and angular momentum. From the joint distribution, we extract marginal distributions of several key parameters using Monte-Carlo integration, and numerically verify them by comparing to an identical ensemble of scattering experiments produced by the FEWBODY code. From the comparison, we identify a regime not represented by the density-of-states formulation: the hard binary regime, where one binary is much harder then the four-body energy scale, and the system acts as an effective three-body system. We hypothesize that at this regime the system's probability distribution spreads over an effective reduced three-body chaotic phase space. The process of transfer from four-body to three-body phase-space is still not understood, and represents the next natural extension of density-of-states methods.
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BibTeX
@misc{zack2026deus,
title = {{Deus Ex Statistica: A Statistical Solution to the binary-binary Outcome of the Chaotic, Non-Hierarchical Four-Body Problem}},
author = {Yoav Zack and Hagai B. Perets and Yonadav Barry Ginat},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09279},
eprint = {2609.09279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09279},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Deus Ex Statistica: A Statistical Solution to the binary-binary Outcome of the Chaotic, Non-Hierarchical Four-Body Problem
AU - Yoav Zack
AU - Hagai B. Perets
AU - Yonadav Barry Ginat
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09279
UR - https://arxiv.org/abs/2609.09279
AB - We present an analytical, statistical solution to the binary-binary (2+2) outcome of the chaotic non-hierarchical four-body problem. The solution is based on the density-of-states formulation pioneered by J. J. Monaghan. The method skips the computationally expensive integration of the equations of motion, and instead samples the outcome from the chaotic phase-space, subject to conservation of energy, momentum, and angular momentum. From the joint distribution, we extract marginal distributions of several key parameters using Monte-Carlo integration, and numerically verify them by comparing to an identical ensemble of scattering experiments produced by the FEWBODY code. From the comparison, we identify a regime not represented by the density-of-states formulation: the hard binary regime, where one binary is much harder then the four-body energy scale, and the system acts as an effective three-body system. We hypothesize that at this regime the system's probability distribution spreads over an effective reduced three-body chaotic phase space. The process of transfer from four-body to three-body phase-space is still not understood, and represents the next natural extension of density-of-states methods.
ER -