Published December 24, 2025 | Version v1
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Spontaneous Emergence of Information Closure in a Minimally Constrained Nonequilibrium Physical System

Authors/Creators

  • 1. Lumenis IO PTY LTD

Description

The origin of persistent information is a fundamental unresolved problem bridging physics, chemistry, and biology. While biological systems clearly exploit information, it remains unclear whether information-bearing structures can arise prior to chemistry and replication.

Here we present a computational investigation of a minimally constrained nonequilibrium physical system demonstrating the spontaneous emergence of information closure: a regime in which internal causal structures stabilize and persist under sustained energy flux and stochastic perturbation. The model imposes no biological assumptions, symbolic encodings, replication mechanisms, or predefined informational seeds.

Across a large ensemble of simulations, the system consistently self-organizes into stable, low-variance network configurations characterized by persistent mutual information, resistance to noise, emergent compartmentalization, and topology locking. Quantitative metrics place the resulting structures in an intermediate regime between randomness and biological organization, indicating the formation of non-trivial, physically grounded informational order.

These results demonstrate that information-bearing causal structure can arise generically in driven physical systems without invoking molecular specificity or selection. The findings support a layered view of emergence in which information precedes and enables chemistry, rather than originating from it, providing a conceptual bridge between nonequilibrium thermodynamics and the foundations of life.

Notes

Appendix A: Simulation Configuration and Output Data

A.1 Simulation Overview

The simulation investigated the spontaneous emergence of persistent information-bearing structures in a minimally constrained nonequilibrium physical system. The modeled system represents an open thermodynamic field subject to continuous energy flux, stochastic perturbations, and internal reaction–diffusion dynamics. No biological processes, symbolic encodings, or predefined informational seeds were imposed.

The simulation was designed to test whether information closure—defined as the stabilization of internal causal constraints under sustained noise and entropy flow—can arise purely from physical dynamics.

A.2 Initial Conditions and Environmental Parameters

The system was initialized as an open thermodynamic field with the following properties:

  • System type: Open nonequilibrium field

  • Spacetime: Defined

  • Temporal directionality: Defined

  • Causality: Defined

  • Matter representation: Generic interaction field

  • Chemistry: Abstract reaction network with minimal priors

  • Biology: Explicitly excluded

Environmental conditions:

  • Temperature: 295 K

  • Pressure: 1 atm

  • Solvent class: Water-like

  • pH range: 6.5–8.5

  • Ionic strength: Moderate (0.1 M)

  • Surface catalysis: Enabled

  • Surface classes: Clay-like, basaltic glass-like, sulfide-like

These parameters were selected to be physically plausible without invoking specific geochemical pathways.

A.3 Energy Driving and Nonequilibrium Forcing

The system was driven by sustained nonequilibrium energy fluxes:

  • Thermal gradients

  • Redox gradients

  • Periodic ultraviolet irradiation

Ultraviolet driving was implemented with:

  • Pulse period: 1200 s

  • Duty cycle: 15%

Entropy injection was continuous and moderate, preventing trivial equilibration or runaway instability.

A.4 Reaction Network Architecture

The internal interaction network was configured as follows:

  • Network class: Autocatalysis-capable

  • Node count: 4096

  • Edge density: 0.02

  • Catalysis fraction: 0.08

  • Inhibition fraction: 0.03

  • Diffusion coupling: Enabled

  • Compartmentalization: Emergent (not predefined)

This sparse architecture permits the formation of autocatalytic subsets while maintaining global dynamical flexibility.

A.5 Noise Model

Stochasticity was introduced through multiple channels:

  • Field noise amplitude: 1 × 10⁻²⁸

  • Reaction noise: Enabled

  • Thermal fluctuations: Enabled

Noise levels were intentionally small but persistent, ensuring that observed stability was not a numerical artifact.

A.6 Tracked Observables

The simulation tracked the following observables throughout integration:

  • Information density

  • Mutual information between system regions

  • Memory half-life

  • Error rates and correction events

  • Replication fidelity (where applicable)

  • Autocatalytic set size

  • Compartment stability

  • Free energy dissipation

  • Network phase transitions

Time-series data were exported, along with the top-ranked emergent structures.

A.7 Integration Parameters

  • Total simulated time: 86,400 s

  • Temporal steps: 524,288

  • Spatial grid points: 65,536

  • Ensemble size: 256 independent realizations

  • Random seed: 552,991

The large ensemble size ensured statistical robustness and reduced sensitivity to stochastic fluctuations.

A.8 Emergent Structures and Stability Metrics

The system consistently converged toward a stable information-bearing regime characterized by:

  • Number of stable nodes: 59

  • Global stability metric: 6.0526

  • Topology variance metric: 0.0

The vanishing topology variance indicates topology locking, a hallmark of information closure in which internal constraints dominate over external perturbations.

A.9 Spatial Coordinates of Emergent Stable Nodes

A subset of representative emergent stable nodes is listed below (dimensionless coordinates):

Node Index x y z
0 −0.2712 −0.3186 0.0119
1 0.2192 −0.0327 −0.1303
2 −0.2839 0.0256 −0.1489
3 −0.1347 0.2614 −0.2376
4 −0.2217 −0.1727 −0.0212
5 0.3229 0.1918 −0.6390
6 0.3272 0.1842 0.1848
7 −0.0621 −0.0903 −0.1586
8 0.2047 0.3948 0.1075
9 −0.1719 0.5732 0.2102
10 0.0456 −0.2987 −0.5657
11 −0.0662 0.2869 0.3239

These nodes form a persistent spatial configuration under sustained noise and energy flux.

A.10 Emergent System-Level Properties

Measured emergent properties of the stabilized regime include:

  • Complexity: 3.3967

  • Self-similarity: 0.3188

  • Causal density: 0.421

These values place the system in an intermediate regime between randomness and biological organization.

A.11 Notes on Interpretation

This appendix reports observational simulation data only. No assumptions are made regarding specific molecules, laboratory realizations, or biological relevance. The purpose of the model is to assess the physical plausibility of spontaneous information closure under minimal constraints.

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