Phase Transitions in Driven Informational Systems: A Two-Field Perspective on Learning Theory and Non-Equilibrium Chemistry

TL;DR

This paper presents a unified framework for understanding phase transitions in driven informational systems, linking deep learning phenomena and non-equilibrium chemistry through a two-field perspective.

Contribution

It introduces a novel two-gradient-field model with specific order parameters, offering a new theoretical lens and testable predictions for phase transitions in complex systems.

Findings

Consistent with recent empirical findings on alignment transitions and adversarial scaling.

Proposes falsifiable predictions that distinguish the two-field model from single-field approaches.

Identifies a candidate universality class with specific scaling exponents.

Abstract

Phase-transition phenomena in deep learning (grokking, emergent capabilities, and ontological reorganization under context shift) have been studied through several lenses, including representational compression, singular learning theory, and information-theoretic progress measures. Independently, non-equilibrium statistical physics has identified phase transitions in driven chemical reaction networks underlying prebiotic selection, with empirical signatures that are difficult to reproduce within single-field gradient accounts. We propose a perspective in which both classes of phenomena admit a common description as driven informational systems: stochastic processes governed by two gradient fields, an entropy production rate Sigma and an information quasi-potential Phi_I := -ln p*, where p* is the stationary density. Within this framework we introduce two candidate order parameters: an adversarial breakdown threshold alpha_dagger and a self-referential coupling threshold kappa_c. The joint scaling of (alpha_dagger, kappa_c) defines a candidate universality class with exponents (gamma_1, gamma_2). We outline the geometric structure of this framework, identify falsifiable predictions distinguishing it from single-field alternatives, and show consistency with recent empirical findings (2024--2026) on alignment transitions, adversarial breakdown scaling, and partial introspection in large language models.