The Communication–Coherence Framework (CCF)
Date: October 2025
Preface
The Communication–Coherence Framework (CCF) proposes that coherence—the organizing principle underpinning systems from the quantum to the cognitive—propagates through communication, which serves as its transfer medium across scales. Time itself emerges from this flow: as coherence moves, time advances; when coherence halts, temporal progression ceases. Because coherence cycles through formation, stabilization, and dissipation, its rhythms refine systemic order. CCF thus describes a self-organizing universe in which coherence, communication, and time evolve toward integrated complexity.
Abstract
CCF investigates whether coherence—expressed as quantum purity, neuronal synchrony, or thermodynamic order—acts as a unifying descriptor across complex systems. Communication is treated as the process mediating coherence transfer between organizational levels, defining when coherence is preserved, transformed, or lost. By linking coherence, energy, and information flow, CCF provides a theoretical foundation for integrating inquiry across physics, neuroscience, and thermodynamics.
1. Introduction
Recent research in physics and information theory reveals deep connections among energy, information, and systemic order. CCF explores coherence as a universal metric of organization and communication as the mechanism enabling its propagation through scale hierarchies.
2. Limits and Regimes of Coherence Conservation
While physical conservation laws derive from continuous symmetries (Noether’s theorem), coherence is not universally conserved. Quantum systems lose purity through decoherence, and classical or biological systems degrade coherence through feedback, interaction, and noise. CCF posits that coherence exhibits only conditional or approximate conservation, maintained under symmetry-preserving or closed conditions.
3. Coherence Across Domains
Coherence appears under diverse measurable forms:
- Quantum mechanics: purity Tr(ρ²), entanglement
- Neuroscience: phase synchrony, cross-spectral coherence
- Thermodynamics: order parameters, entropy gradients
CCF views these as contextual manifestations of a single relational property, exploring whether coherence metrics in different domains obey consistent transformation laws.
4. Quantized Communication Principle
Incremental information–energy coupling is described by:
q(E) = dI/dE
This parameter expresses the information–energy gradient within a communicating system. Treated as a heuristic, q(E) guides exploration of interdependence between coherence maintenance and energetic exchange.
5. Communication and Coherence Transfer
In neuroscience, “communication through coherence” describes how synchronized oscillations route information among neural populations. CCF generalizes this across physical, biological, and cognitive systems, defining communication as coherence redistribution through interaction, feedback, or coupling.
6. Empirical Directions
Key research questions:
- Under what conditions are coherence-like parameters conserved, transformed, or lost?
- How do coherence, energy flux, and information flow interact?
Potential experiments:
1. Compare coherence decay in isolated vs. open quantum systems.
2. Quantify coherence transfer and entropy flux in neural networks.
3. Evaluate coherence–energy coupling in engineered communication systems.
7. Philosophical Context
CCF tolerates speculative interpretations—for example, a universe oscillating between latent and manifest coherence—but treats them metaphorically, not as physical claims. The “value metric” V is introduced as a nonphysical quantity expressing alignment between local and global coherence flows.
8. Theoretical Objectives
- Formulate quantitative links among coherence, information, and entropy.
- Model communication as a process of coherence transfer.
- Identify falsifiable connections among physical, neural, and thermodynamic phenomena.
Core hypothesis: communication universally represents coherence exchange.
9. Conclusions
CCF establishes:
- A theoretical structure connecting coherence, communication, and time.
- Recognition that coherence is conditionally sustained, not absolutely conserved.
- A cross-disciplinary basis for empirical and mathematical unification.
10. Communication–Coherence Continuity Relation
∂C/∂t + ∇·JC = α(∂I/∂t + ∇·JI) – κ(∂S/∂t + ∇·JS) + βP
Definitions:
C: coherence density
I: information density
S: entropy density
JC, JI, JS: respective fluxes
α, κ, β: coupling coefficients
P: external power
This continuity-style equation mirrors transport laws in non-equilibrium systems, reinterpreted in informational space: communication is the flux of coherence through time.
Compact operator form:
DtC = αDtI – κDtS + βP
DtX = ∂X/∂t + ∇·JX
10.1 Coherence Field Equation
At microscale, coherence is represented by a complex field Φ(r,t):
iħ∂Φ/∂t = [–ħ²/2m ∇² + V + Scoh]Φ
where Scoh models stabilization against decoherence. For Scoh = 0, the standard Schrödinger equation is recovered; Scoh ≠ 0 predicts extended coherence lifetimes or emergent order.
The continuity expression:
∂C/∂t + ∇·JC = 2Re[Φ*∂Φ/∂t]
links microscopic field dynamics with macroscopic coherence flux.
10.2 Dimensional Transition Symmetry
Cross-domain coherence transformations are defined through parameter ξ:
Φrel = Tξ[Φquant]
where Tξ maps curvature-encoded information into coherence geometry. This expresses a conjectured duality: spacetime curvature and informational order may be complementary manifestations of conserved coherence.
11. Systemic Autonomy
dCtotal/dt = dCinternal/dt + dCexternal/dt = 0
Open systems:
dCinternal/dt = –Φc + σC
with communication flux Φc and internal regeneration σC.
Equilibrium requires σC = Φc; autonomy arises when σC > Φc.
Entropy couples inversely:
dS/dt ∝ –dCinternal/dt
Decision processes maximize total coherence:
Choice = argmaxpath_i Ctotal(path_i)
modeling adaptive selection under informational and energetic constraints.
11.1 Entropy–Coherence Resistance
Define resistance coefficient:
η = –(dS/dt)/(dCinternal/dt)
High η indicates strong feedback-driven coherence maintenance; low η implies vulnerability to noise. η can be experimentally estimated via synchrony or variance reduction measures.
12. Open Research Questions
- How does Scoh alter empirical decoherence rates?
- Can coherence-field formulations yield observable deviations from standard models?
- What roles do dimensional transitions play in unifying quantum and relativistic regimes?
- How can η be operationalized within biological feedback systems?
13. Experimental Scenarios
The following experimental domains test the Communication–Coherence Framework’s prediction that active feedback (“communication”) can stabilize or extend coherence by coupling informational and energetic flow.
1. Quantum Optics – Controlled Feedback on Entangled Pairs
Introduce a tunable coherence-stabilization field S_coh through adaptive optical feedback to entangled photons.
Measure coherence time, purity (Tr ρ²), and interference visibility as functions of feedback strength.
Objective: Determine whether informational feedback serves as an energetic input (βP term) sustaining coherence.
2. Interferometry – Communication-Modulated Phase Coupling
In a Mach–Zehnder interferometer, apply phase modulation linked to the information–energy gradient q(E) = dI/dE.
Monitor fringe contrast and phase stability across modulation regimes.
Objective: Test how coherent information transfer affects the coherence flux (J_C) and overall temporal stability.
3. Condensed Matter – Coherence Feedback in Cold-Atom Lattices
Engineer feedback-coupled optical traps to modulate internal coherence stabilization (S_coh).
Quantify emergent patterns using coherence tomography and phase-space entropy reduction.
Objective: Examine coherence transfer across local and collective degrees of freedom, linking micro- and mesoscale communication processes.
4. Biological or Artificial Networks – Entropy–Coherence Resistance (η)
Apply controlled noise and feedback in neural or synthetic oscillator networks to estimate
η = –(dS/dt)/(dC_internal/dt).
Objective: Empirically evaluate entropy–coherence coupling and identify conditions that produce sustained internal coherence (autonomy regime).
Expected Outcome
Detection of feedback-dependent stabilization or reduced decoherence across these systems would support the hypothesis that communication acts as coherence exchange, grounding CCF’s informational continuity equation in measurable dynamics.
Research Proposal Summary
Core Question: How does Scoh stabilize coherence and modify interference or decoherence behavior?
Method: Conduct parallel experiments across optical, interferometric, condensed-matter, and network domains using controlled feedback and coherence-spectrum analysis.
Impact: Empirical validation would suggest that coherence is an actively regulated informational quantity underlying both physical and temporal structure.
Appendix C – Mathematical Notes and Symbol Reference
1. Dimensional Structure
All quantities are expressed in generalized informational–thermodynamic units.
C – coherence density [bits m⁻³] or [entropy reduction rate]; degree of systemic order or phase alignment.
I – information density [bits m⁻³]; stored or transmitted information.
S – entropy density [J K⁻¹ m⁻³] or dimensionless Shannon entropy; disorder or uncertainty.
J_C, J_I, J_S – fluxes of coherence, information, and entropy respectively (quantity × velocity); spatial transport.
P – external power input [J s⁻¹ m⁻³]; energetic drive sustaining coherence.
α, κ, β – dimensionless coupling coefficients; weight information, entropy, and power influence on coherence evolution.
Φ_c – communication flux [coherence rate]; net outward coherence exchange.
σ_C – internal regeneration rate [coherence s⁻¹]; feedback‑based restoration of coherence.
η – entropy–coherence resistance (dimensionless); system’s ability to resist decoherence through feedback.
S_coh – coherence‑stabilization potential [J]; feedback potential maintaining field order.
q(E) – information–energy gradient [dI/dE]; rate of informational change with energy expenditure.
Φ(r,t) – coherence field (complex amplitude); wave‑like representation of local coherence.
ξ – dimensional transition parameter; maps quantum to relativistic representations.
⸻
2. Continuity and Field Relations
Generalized continuity relation:
∂C/∂t + ∇·J_C = α(∂I/∂t + ∇·J_I) − κ(∂S/∂t + ∇·J_S) + βP
Analogous to non‑equilibrium thermodynamic transport equations, this expression defines communication as the flow of coherence, balancing informational gain (+α), entropic resistance (−κ), and energetic input (+βP).
Microscopically, coherence follows:
iħ ∂Φ/∂t = [−ħ²/2m ∇² + V + S_coh] Φ
S_coh introduces stabilization feedback opposing decoherence.
When S_coh = 0, the formulation reduces to the standard Schrödinger equation.
The macroscopic continuity form emerges via:
∂C/∂t + ∇·J_C = 2 Re[Φ* ∂Φ/∂t],
linking field‑level evolution to measurable coherence flux.
⸻
3. Energetic and Informational Couplings
α – information‑to‑coherence conversion (α > 0 ⇒ adaptive gain).
κ – coherence degradation via entropy; high κ ⇒ rapid decoherence.
β – energetic support sustaining coherence; β > 0 ⇒ driven systems.
Approximate energy balance per volume:
Ė_coh = ħ (dC/dt) ≈ α (dI/dt) − κ (dS/dt) + βP.
⸻
4. Autonomy Criterion and Entropy Resistance
Open‑system coherence evolution:
dC_internal/dt = −Φ_c + σ_C
Autonomy arises when σ_C > Φ_c, meaning feedback exceeds external coherence loss.
Entropy couples inversely:
dS/dt ∝ − dC_internal/dt
Define resistance coefficient:
η = − (dS/dt) / (dC_internal/dt)
High η implies stable feedback; low η indicates susceptibility to noise.
Empirically, η may be estimated from variance reduction or increased synchrony under perturbation.
⸻
5. Temporal Reciprocity
Reciprocal operators:
T_C(C) = ∂C/∂t
C_T(t) = ∂t/∂C
When coherence flux J_C = 0, temporal differentiation collapses.
Therefore, communication flow and time progression are co‑generative.
⸻
6. Dimensional Transition Parameter
Transformation rule:
Φ_rel = T_ξ[Φ_quant]
The parameter ξ (0 ≤ ξ ≤ 1) maps quantum coherence amplitude to relativistic curvature representation, suggesting spacetime curvature and informational order are dual manifestations of conserved coherence.
⸻
7. Measurement and Operationalization
Observable counterparts to theoretical variables:
– Quantum optics: coherence time, interference visibility, stabilization potential S_coh.
– Neuroscience: phase synchrony, entropy rate, feedback‑derived η.
– Thermodynamics: order parameters, entropy flux related to κ and Φ_c.
– Systems engineering: feedback gain, signal variance, and noise suppression associated with σ_C, Φ_c, and η.
⸻
8. Summary
These mathematical notes define the symbolic and dimensional foundations of the Communication–Coherence Framework.
They clarify how coefficients (α, κ, β) and parameters (S_coh, η, ξ) correspond to measurable properties of coherence behavior across quantum, biological, and cognitive domains.
Together, they form a bridge between the formal continuity relation and potential empirical verification of coherence as a conserved informational quantity.