A Universal Constraint on Informational Systems
Author: Kevin L. Brown, Independent Researcher
Date: December 2025
DOI: 10.5281/zenodo.17771878
Introduction:
Why So Many Systems Become More Ordered Over Time — and Why We Cannot Explain… It Until Now
Modern science excels at modeling separate domains. Yet the deeper question of why complex systems stabilize and become more coherent remains unanswered.
Across disciplines, we observe the same striking pattern:
- Quantum systems collapse into more coherent eigenstates.
- Biological networks synchronize and develop stable feedback structures.
- Neural systems self-organize into coherent modes.
- Dynamical systems contract into stable attractors.
- Astrophysical structures form persistent geometric boundaries.
- Information-processing systems minimize noise and maximize structure over time.
Despite these parallel behaviors, no discipline provides a single explanation for why coherence increases so reliably across scales.
Current theories point to:
- entropy in thermodynamics,
- decoherence in quantum mechanics,
- feedback in biology,
- attractors in nonlinear dynamics,
- curvature and stability in astrophysics.
But these are local explanations, not a universal mechanism.
Why do such different systems display the same trajectory—
a persistent move toward higher coherence?
This paper introduces the first general answer.
The Core Leap: Coherence Expansion as a Universal Informational Constraint
The breakthrough principle of this work is straightforward:
Any self-maintaining informational system must evolve toward higher internal coherence to remain stable.
This idea is formalized in the Coherence Expansion Principle (CEP).
CEP states that on any informational manifold I=(M,F,O),I = (M, F, O),I=(M,F,O),
the coherence functional C[F]\mathcal{C}[F]C[F]
is monotonically non-decreasing under all allowable operations.
In simpler terms:
Coherence cannot decrease without the system losing stability or identity.
This is not a new physical force or a metaphysical claim.
It is a structural requirement for systems that:
- preserve state across time,
- propagate information forward,
- and maintain internal consistency.
CEP provides the first unified explanation for coherence growth across scales.
What CEP Actually Explains
CEP reframes long-standing puzzles across disciplines using one structural rule.
1. Why quantum systems collapse into stable eigenstates
Projection increases the system’s internal coherence, consistent with CEP.
2. Why biological systems develop synchrony and reflective capacity
Networks that enhance coherence persist; those that lose it decay.
3. Why dynamical systems converge into attractors
Attractors represent coherence-maximizing configurations.
4. Why large-scale structures stabilize into boundaries and persistent patterns
Stable astrophysical structures correspond to coherence-dense regions in informational curvature.
5. Why time-domain signals show emergent modulation and phase alignment
CEP predicts that scalar-time evolution preferentially amplifies coherence-preserving modes.
Across scales, coherence expansion explains how systems retain identity while undergoing internal change.
The Scientific Questions CEP Answers
CEP directly addresses three foundational questions left open across scientific domains:
Question 1:
Why do systems with different physical substrates—quantum, biological, dynamical, astrophysical—show similar coherence growth behaviors?
Answer:
Because coherence expansion is substrate-independent.
It applies to any system represented informationally.
Question 2:
Why do stable systems persist while others disintegrate or enter chaotic regimes?
Answer:
Because only coherence-preserving transformations remain dynamically stable.
Systems that allow coherence to fall lose their identity.
Question 3:
Is there a single mathematical condition that universally governs structure formation and stability?
Answer:
Yes. The coherence functional C[F]\mathcal{C}[F]C[F] is the universal invariance.
CEP identifies its monotonic behavior across all allowable operations.
Implications if CEP Is True
If CEP is correct, the implications are significant—not speculative, but structural.
1. Coherence is the deepest organizing principle of complex systems
Not energy, not entropy, not complexity: coherence.
2. Cross-domain parallels become expected, not mysterious
Quantum, biological, and dynamical systems behave similarly because they obey the same informational constraint.
3. System evolution can be understood through coherence landscapes
High-coherence regions act as attractors across domains.
4. Stability becomes mathematically predictable
CEP defines which transformations preserve identity and which do not.
5. Coherence can be measured, compared, and falsified across systems
CEP does not predict outcomes; it constrains the allowable pathway of evolution.
6. Time acquires a structural, not absolute, interpretation
Scalar-time evolution is coherence-weighted, explaining non-linear temporal behavior in many systems.
Why the Coherence Expansion Principle Is Not “Just Another Stability Theory”
CEP differs from conventional frameworks in three critical ways.
1. It provides a single generative mechanism
Coherence increase arises from:
- the same functional C[F]\mathcal{C}[F]C[F],
- the same curvature metric,
- the same operator family OOO,
- the same informational geometry.
One mechanism, many domains.
2. It is fully falsifiable
CEP fails if:
- a system consistently decreases C[F]\mathcal{C}[F]C[F] under allowable evolution,
- long-term attractor formation violates coherence monotonicity,
- informational curvature does not correspond to stable configurations.
CEP’s predictions are measurable in laboratory, biological, and astrophysical systems.
3. It integrates multiple informational theories into a single narrative
CEP unifies insights from:
- informational geometry,
- dynamical systems theory,
- network theory,
- quantum information,
- complex systems stability,
- time-domain analysis.
CEP is not a new physical law:
it is a universal informational constraint underlying known laws.
The Bigger Picture
If CEP is correct, the universe reveals itself as an informationally coherent hierarchy, not a collection of isolated systems.
Across scales, we see:
- structures forming,
- boundaries stabilizing,
- networks synchronizing,
- attractors converging,
- coherence increasing.
CEP provides the first mathematically explicit reason why.
The universe is not merely evolving.
It is structurally organizing.
What we call “order,” “stability,” “identity,” or “structure” are all expressions of a single principle:
Coherence expands.
And for the first time, CEP gives us a formal way to understand how—and why—that happens.