Information bounds the robustness of self-organized systems

TL;DR

This paper establishes fundamental information-theoretic bounds on the robustness of self-organized systems, showing how noise and correlations influence their capacity to form stable structures.

Contribution

It introduces a theoretical bound on positional information in noisy self-organized systems and demonstrates how boundary effects and long-range correlations can affect this limit.

Findings

Positional information capacity obeys an area law bound.

Fine-tuning transport coefficients saturates the bound.

Long-range correlations can bypass the bound through global constraints.

Abstract

Self-organized systems, from synthetic nanostructures to developing organisms, are composed of fluctuating units capable of forming robust functional structures despite noise. Here, we ask: are there fundamental bounds on the robustness of noisy self-organized systems? By viewing self-organization as noisy encoding, we prove that the positional information capacity of short-range classical systems with discrete states obeys a bound reminiscent of area laws for quantum information. We illustrate this principle with lattice models whose dynamics is captured by continuum models derived using exact coarse-graining techniques and validated through Dynamical Renormalization Group calculations. The universal bound is saturated by fine-tuning transport coefficients, which can be rationalized in the continuum limit upon considering the effects of boundaries on domain wall dynamics. We illustrate how this limit can be bypassed when long-range correlations are present by investigating a wave-pinning model motivated by biological mechanisms. In this class of models, global constraints reduce the need for fine-tuning by providing effective integral feedback. Our work identifies fundamental limits for the ability of natural and synthetic microsystems to self-assemble into patterns and rationalizes them on purely information-theoretic grounds.