# On Principles of Emergent Organization

arXiv: https://arxiv.org/abs/2311.13749 · HTML: https://mlsanity.com/paper/2311.13749/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 228 references that are in the map.
- First posted on arXiv 23 Nov 2023.

## Builds on (most cited first, 2 of 2)

- [Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems](https://mlsanity.com/paper/2111.14889/) (2021)
- [DisCo: Physics-Based Unsupervised Discovery of Coherent Structures in Spatiotemporal Systems](https://mlsanity.com/paper/1909.11822/) (2019)

## Built on by (most cited first, 4 of 4)

- [Large Language Models and Emergence: A Complex Systems Perspective](https://mlsanity.com/paper/2506.11135/) (2025)
- [Deep Koopman operator framework for causal discovery in nonlinear dynamical systems](https://mlsanity.com/paper/2505.14828/) (2025)
- [The Physics of Learning: From Autoencoders to Truly Autonomous Learning Machines](https://mlsanity.com/paper/2407.04700/) (2024)
- [Inferring Kernel ε-Machines: Discovering Structure in Complex Systems](https://mlsanity.com/paper/2410.01076/) (2024)

## Abstract (arXiv)

After more than a century of concerted effort, physics still lacks basic principles of spontaneous self-organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then, an overview of two modern mathematical formulations of organization -- intrinsic computation and evolution operators -- lays out a way to overcome these challenges. Together, the vantage point they afford shows how to account for the emergence of structured states via a statistical mechanics of systems arbitrarily far from equilibrium. The result is a constructive path forward to principles of organization that builds on mathematical identification of structure.