The Communication–Coherence Framework
A Unified Model of Coherence Transfer, Communication, and Emergent Dynamics
Cory C. Laughlin
December 14, 2025
Unified Manuscript: Core Theory + Empirical Validation Framework
Abstract
The Communication–Coherence Framework (CCF) treats coherence as a dynamical quantity that can be
transported, regenerated, and dissipated through communication. This manuscript presents a unified treatment
combining: (1) a tightened mathematical core grounded in continuity equations and non-equilibrium transport,
(2) concrete operationalizations in engineered and neural systems, and (3) a coherent empirical validation
strategy spanning quantum optics, interferometry, and condensed-matter systems. CCF proposes that
coherence, information, and entropy are jointly coupled through a generalized continuity relation, and that
effective mechanisms of coherence stabilization can reduce dissipative losses under specific conditions. The
framework is presented as a coarse-grained phenomenological model with clear assumptions, explicit null
hypotheses, and mapped pathways to testable predictions. Extensions to time, causality, and quantum collapse
are developed as interpretive and speculative layers built on the validated core.
1. Introduction
Advances in physics and information theory reveal profound connections among energy, information, and order
across physical and biological systems. The Conservation of coherence—the degree of ordered structure in a
quantum or classical system—is not universal. Quantum systems lose coherence (purity) through decoherence;
classical systems may gain or lose coherence through feedback, interaction, or noise. This raises a
fundamental question: under what conditions can coherence be preserved, transferred, or regenerated?
The Communication–Coherence Framework (CCF) investigates coherence as a general dynamical descriptor.
It proposes that communication mediates coherence transfer between levels of organization and examines
when coherence is maintained or dissipated. Rather than treating coherence as a derivative property, CCF
models it as a transportable quantity governed by continuity-style equations analogous to non-equilibrium
thermodynamics and active-matter transport.
This unified manuscript integrates three components: (1) a tightened mathematical core defining the central
continuity relation with explicit assumptions and dimensions, (2) operationalizations for engineered, neural, and
quantum systems, and (3) a coherent research proposal for empirical testing. The framework is intentionally
positioned as a coarse-grained phenomenological model, not as a claim of new fundamental fields or laws.
2. Core Mathematical Framework
2.1 Central Continuity Relation
At the heart of CCF is a continuity-style equation governing how coherence evolves under information, entropy,
and energy exchange. Let C(x,t), I(x,t), and S(x,t) denote coherence, information, and entropy densities (per
unit volume), with associated fluxes JC, JI, JS. The Communication–Coherence continuity relation is:
∂C/∂t + ∇·JC = α ∇·JI − κ ∇·JS + β P
where P represents external power input, and α, κ, β are system-specific coupling coefficients. This equation
generalizes non-equilibrium transport laws by treating communication as the flux of coherence in time, with
information flow acting as a source and entropy flow as an effective sink.
Structural connection: The CCF continuity law parallels non-equilibrium thermodynamic transport and
active-matter continuity equations, but extends them by treating coherence as the transported quantity and by
explicitly coupling to information and entropy fluxes.
Units and dimensions: C, I, and S are treated as densities per unit volume. C is a dimensionless coherence
index per unit volume; I is information density (bits/volume); S is entropy density (bits/K/volume or J/K/volume).
The fluxes JC, JI, JS have units of density per unit time. The coupling coefficients α, κ, β are dimensionless or
have units chosen so that each term in the continuity equation has dimensions of C per unit time. Full
dimensional analysis is provided in Appendix C.2.
Modeling ansatz: The appearance of ∇·JI and ∇·JS as driving terms is a deliberate modeling choice. CCF
assumes that spatially structured divergences of information and entropy flux act as effective sources and sinks
for coherence, rather than treating I or S as explicit local production terms. Alternative formulations with
production terms (e.g., +αI − κS) are mathematically possible and may be more appropriate in certain regimes;
the present choice is adopted for consistency with transport-style equations in non-equilibrium statistical
mechanics and to facilitate empirical fitting from measurable flux gradients.
2.2 Radiative and Scalar Coherence Channels
To distinguish conventional, lossy propagation from hypothetical reduced-loss channels, the coherence and
information fluxes are decomposed into radiative and scalar components:
JC = Jrad
C + Jscalar
C; JI = Jrad
I + Jscalar
I
A scalar-mode participation coefficient χ ∈ [0,1] encodes the effective fraction of coherence exchange occurring
through non-radiative channels. The entropy coupling is promoted to a mode-dependent term κeff(χ), which
decreases as χ → 1, so that in the scalar-dominated limit entropy-driven loss is minimized, whereas χ → 0
recovers the standard radiative, dissipative regime.
Important clarification: The scalar channel and χ are introduced as an effective reduced-loss parametrization
of coherence transfer at the coarse-grained level, not as a claim of an additional fundamental physical field
beyond established quantum and classical mechanics. They serve to capture, in phenomenological terms,
regimes where coherence behaves as if transported with suppressed entropy coupling—a useful abstraction for
modeling and prediction, pending empirical validation. This positioning is analogous to concepts like effective
mass or order parameters in condensed-matter physics.
Null hypothesis and reduction: In the limit χ = 0 and with coherence stabilization σC = 0, the framework
reduces to a standard radiative, dissipative transport picture equivalent to conventional decoherence and
open-system treatments, providing a clear baseline against which any putative CCF effects must be tested.
2.3 Coherence Stabilization and Field Formulation
CCF introduces a coherence stabilization term σC (often written as Γ) to represent active or structural
processes that regenerate coherence against decoherence. In field form, a coherence field Φ is used to
represent the unified coherence structure underlying quantum and relativistic descriptions. An
informational–thermodynamic Lagrangian density is defined so that the Euler–Lagrange equations for Φ yield
local continuity expressions for C and its fluxes. In this formulation, coherence stabilization appears as an
additional source term that can counterbalance entropy-driven degradation in appropriate regimes.
2.4 Time–Communication Reciprocity
Within CCF, time is treated as an emergent parameter measuring ordered changes in coherence across the
communication manifold. The continuity relation implies that temporal structure arises from coherence flux: in
regions where JC = 0, coherence becomes stationary and time is locally degenerate, whereas increasing
coherence flux differentiates temporal structure. An effective time–communication reciprocity is expressed by
treating temporal continuity and communication as mutually generative operators, such that equilibrium in
coherence flux corresponds to the limit where local time ceases to progress operationally. This statement is
interpretive and operational; it concerns measurable absence of ordered change in coherence, not literal
disappearance of spacetime dimensions.
3. Minimal Toy Model Implementation
To ground the continuity equations in a concrete, numerically explorable setting, consider a 1D lattice or
network of N nodes, each with a scalar coherence index Ci(t) representing local order (e.g., normalized phase
coherence of an oscillator cluster).
Setup: The coherence flux between neighbouring nodes is modeled as JC,i→i+1
∝ Ci − Ci+1, so that ∇·JC
reduces to nearest-neighbour differences on the graph. Information and entropy fluxes are instantiated as
analogous network flows derived from signal amplitudes or noise levels, and the scalar participation χ enters as
a factor that partially redirects coherence exchange into an effective reduced-loss channel on selected edges.
In this discrete setting, the CCF continuity relation becomes a set of coupled difference equations for Ci(t),
allowing straightforward numerical exploration of how varying α, κ, β, and χ affects coherence spreading,
stabilization, and decay in a controlled, interpretable model.
Value: This toy model serves as a bridge between abstract theory and empirical measurement. It permits direct
simulation of predicted coherence dynamics, comparison with engineered oscillator networks, and iterative
refinement of coupling parameters.
4. Measurement and Operationalization
To connect CCF to empirical systems, coherence and its flux must be instantiated as measurable quantities in
specific domains. The following operationalizations enable direct testing of CCF predictions.
4.1 Engineered Systems (Oscillators, Communication Networks)
In oscillator networks or communication hardware, C can be operationalized as a normalized order parameter
(e.g., Kuramoto-type phase coherence or spectral coherence between channels). The coherence flux JC is
estimated from spatial or network gradients in this order parameter over time, allowing direct comparison of the
model to measurable network synchrony evolution. This provides a clear pathway for testing the core continuity
relation in well-controlled systems.
4.2 Neural Systems
In neural data, C is operationalized via phase-locking values (PLV) or cross-spectral coherence between brain
regions. The coherence flux JC is approximated from changes in coherence along anatomical or functional
connectivity graphs, using time-resolved measures such as sliding-window PLV or weighted phase-lag index
(wPLI). This approach enables testing of CCF predictions against EEG/MEG and fMRI time series, particularly
during attention-demanding or integrative cognitive states where coherence-based communication is
hypothesized to be prominent.
5. Scope and Regime of Validity
This core framework is intended as a coarse-grained, phenomenological description. Coherence is not
assumed to be universally conserved; approximate conservation arises only under closed or
symmetry-preserving conditions, and the coupling coefficients α, κ, β and scalar participation χ are understood
as empirically determined parameters, not universal constants. In this way, CCF stays continuous with
established quantum and thermodynamic formalisms while proposing a specific, testable structure for how
communication, information, and entropy jointly govern coherence evolution.
5.1 Core Assumptions and Limits
Coarse-grained description: Coherence C, information I, and entropy S are treated as effective densities
and fluxes over coarse-grained volumes, not as microscopic observables for individual particles or degrees
of freedom.
Conditional, not universal, conservation: Coherence is not assumed to be a fundamental conservation
law; the continuity relation allows source and sink terms, and approximate conservation appears only in
effectively closed or symmetry-preserving regimes.
Empirical coupling coefficients: The parameters α, κ, β and the scalar participation coefficient χ are
phenomenological and system-dependent; they must be inferred or fit from experiment rather than
assumed universal constants.
Flux-divergence ansatz: The choice to drive coherence evolution via ∇·JI and ∇·JS is a modeling
assumption; alternative formulations (e.g., with explicit production terms) may be more suitable in some
regimes and should be explored empirically.
Mode decomposition as effective parametrization: The radiative/scalar split and χ-dependent entropy
coupling are effective reduced-loss models, not claims of new fundamental fields; they capture
coarse-grained regimes and are validated by fit to data.
Standard causal structure: The framework assumes a standard relativistic causal structure with no
superluminal signaling; retrocausal behavior arises only as global boundary-condition constraints in the
variational formulation, not as backward-in-time communication.
Time as emergent, operational: Statements about time 'degenerating' when JC = 0 are interpretive and
operational: they concern the absence of measurable ordered change in coherence, not the literal
disappearance of a spacetime dimension.
Domain of application: The continuity equations and stabilization terms are intended as testable models
for quantum, thermodynamic, and neural/engineered systems where coherence measures and fluxes are
experimentally accessible; extensions to cosmology, afterlife, philosophical value, or simulation hypothesis
are treated as speculative interpretive layers built on top of this core, with clearly marked conceptual gaps
and no empirical grounding in the current document.
6. Empirical Validation Strategy
The following conceptual experimental designs demonstrate how CCF could be empirically explored through
measurable deviations from baseline quantum and thermodynamic predictions, coherence modulation, and
emergent structure formation.
6.1 Example 1: Decoherence Rate Deviation in Quantum Optics
Objective: Test if introducing coherence stabilization affects quantum decoherence rates beyond
environmental contributions.
Setup: Use a photonic quantum optics system with entangled photons.
Method: Prepare entangled photon pairs, then introduce controlled environmental noise with and without
coherence stabilization via engineered feedback or interaction protocols.
Measurement: Detect photon coherence times and entanglement visibility using interferometric methods.
Expected Outcome: Observable deviations in decoherence rates or entanglement decay when stabilization
mechanisms are present versus baseline models. Falsification criterion: no significant deviation from standard
open-system theory.
6.2 Example 2: Interference Pattern Modulation in an Interferometer
Objective: Determine if CCF coherence field effects modulate interference fringes in a Mach–Zehnder
interferometer.
Setup: Mach–Zehnder interferometer with controllable phase shifts.
Method: Implement mechanisms mimicking coherence stabilization effects in one arm, for example via
dynamic phase modulation tied to predicted parameters (e.g., χ-dependent corrections to phase evolution).
Measurement: Record interference patterns with high-resolution photodetectors; analyze fringe contrast,
visibility, and phase shifts.
Expected Outcome: Detectable changes in fringe visibility or phase consistent with CCF predictions.
Falsification criterion: no observable modulation beyond instrumental noise.
6.3 Example 3: Emergent Structure Observation in Condensed Matter
Objective: Observe emergent coherence-driven structures consistent with CCF coherence dynamics in
many-body systems.
Setup: Utilize cold atom lattices or Bose–Einstein condensates.
Method: Manipulate coherence parameters via external fields or inter-particle interactions; introduce controlled
entropy coupling and observe response.
Measurement: Use time-of-flight imaging or coherence tomography to capture emergent structure formation
dynamics.
Expected Outcome: Novel structural or coherence signatures differing from current models, validating CCF
mechanisms of emergence. Falsification criterion: structures consistent with standard equilibrium or existing
non-equilibrium models.
6.4 Refinement Strategy
• Tailor experimental parameters quantitatively based on CCF's mathematical formulations and toy model
simulations.
• Collaborate with experimental physicists to assess technical feasibility and instrumentation.
• Prepare detailed simulation models to predict expected results and refine hypotheses iteratively.
• Develop control experiments that isolate CCF-specific predictions from conventional
quantum/thermodynamic effects.
• Apply statistical frameworks (variance reduction, ANOVA, spectral coherence mapping) to assess
significance of observed deviations.
7. Connections to Existing Frameworks
CCF is designed to interface with and extend established theoretical frameworks without contradicting them.
Quantum Mechanics: The limit χ = 0, σC = 0 recovers open-system quantum dynamics described by the
Lindblad master equation. CCF's entropy coupling term acts as a generalization of Lindblad jump operators,
replacing statistical averaging with explicit communication-entropy coupling mechanisms.
Non-Equilibrium Thermodynamics: The continuity structure parallels transport equations for conserved
quantities (energy, momentum, particles), with coherence treated as a transported quantity in the informational
domain rather than the material domain.
Neuroscience (Communication Through Coherence): CCF formalizes the hypothesis that neural
communication can be mediated by dynamic coherence among brain regions, extending the concept from a
phenomenological observation to a quantitative framework tractable in neural recordings.
8. Speculative Extensions and Clear Conceptual Boundaries
Beyond the core framework, several interpretive and speculative extensions have been explored in earlier
drafts of this work. These are explicitly marked as non-empirical and positioned as conceptual scaffolding for
future development, not as part of the falsifiable theory.
Wave Function Collapse as Coherence Transition: An interpretive mapping of sudden collapse to
gradual coherence dissipation via entropy-communication imbalance, consistent with decoherence theory
but offering alternative language.
Time, Retrocausality, and Boundary Conditions: A variational formulation where temporal structure
emerges from coherence gradients, and retrocausal effects arise from global boundary conditions rather
than backward signaling.
Dimensional Transitions: A speculative hypothesis that transitions between quantum and relativistic
regimes correspond to changes in coherence flow across domains (not empirically grounded).
Consciousness and Value Metaphor: An interpretive metaphor in which a 'value metric' V represents
alignment between local and global coherence flows (purely philosophical, no measurable correlate
proposed).
Simulation Hypothesis: A philosophical musing that universal coherence properties could relate to
informational structure of reality (not a testable claim).
Boundary: None of these extensions are required to validate the core CCF. None are part of the primary
research proposal. All are presented here solely for completeness and to clarify the distinction between the
testable core and speculative interpretation. The core CCF, by contrast, makes only claims about coherence
transport, coupling to information and entropy, and measurable coherence dynamics in well-defined physical
systems.
9. Research Objectives and Outlook
This unified manuscript proposes that CCF serves as a bridge framework connecting quantum mechanics,
thermodynamics, and neuroscience through a common language of coherence transport and communication.
The primary research objective is to determine whether coherence can be meaningfully treated as a
transportable, measurable quantity with coupling to information and entropy that differs from conventional
open-system quantum mechanics only when active stabilization mechanisms are present.
Secondary objectives include: (1) identifying conditions under which coherence conservation becomes
approximate even in open systems, (2) developing quantitative methods to extract coherence fluxes from
neural and engineered data, (3) testing the hypothesis that feedback-controlled coherence stabilization can
exceed predictions of standard dissipative models, and (4) establishing whether effective reduced-loss
transport (the scalar channel regime) arises naturally in any biological or engineered system.
If empirical evidence supports deviations from baseline models in any of the three experimental domains
outlined above, CCF would provide a unified framework for understanding when and how coherence can be
stabilized or transported with reduced dissipation. This could have implications for quantum technologies,
neural information processing, and design of communication systems. Conversely, null results would clarify the
limits of coherence-based descriptions and motivate refinement or rejection of the framework.
10. Summary and Recommendations for Submission
The Communication–Coherence Framework, as presented in this unified manuscript, offers: • A disciplined,
dimensionally consistent mathematical core grounded in continuity equations and non-equilibrium transport
analogy. • Explicit modeling assumptions, null hypotheses, and clear boundaries between testable and
speculative content. • Concrete operationalizations in engineered, neural, and quantum systems, enabling
direct empirical testing. • A refined conceptual positioning of novel elements (scalar channels, coherence
stabilization) as effective parametrizations rather than new fundamental fields. • A coherent research proposal
connecting theory to three concrete experimental domains (quantum optics, interferometry, condensed matter).
This framework is now positioned for submission to interdisciplinary physics, non-equilibrium systems, quantum
optics, or neuroscience journals. It does not claim to be fundamental physics suitable for PRL or Nature
Physics, but rather positions itself as a testable phenomenological model in the spirit of effective-field and
non-equilibrium statistical mechanics traditions.
Recommended submission strategy: 1. Submit the core (Sections 1–7) to an interdisciplinary journal (e.g.,
Journal of Physics: Complexity, Entropy, Frontiers in Physics). 2. Reserve experimental proposals (Section 6)
for specialist venues (quantum optics, neural dynamics, condensed matter) once collaborators are identified. 3.
Archive speculative extensions (Section 8) separately as philosophical commentary or future work, not as part
of the primary submission. 4. Use feedback from reviewers to refine assumptions, particularly around the
empirical interpretability of χ and the scalar channel.
Symbol Definition Units
C(x,t) Coherence density dimensionless/volume
I(x,t) Information density bits/volume
S(x,t) Entropy density bits/K·volume or J/K·volume
J_C, J_I, J_S Fluxes of coherence, information, entropy density/time
α, κ, β Coupling coefficients (system-dependent) dimensionless or appropriate scaling
P External power input energy/time
χ Scalar-mode participation coefficient [0, 1]
σ_C or Γ Coherence stabilization term 1/time
Φ Coherence field (field formulation) field variable
κ_eff(χ) Effective entropy coupling (mode-dependent)varies with χ
Appendix A: Notation and Symbols
Appendix B: Dimensional Analysis (Summary)
The continuity relation ∂C/∂t + ∇·J_C = α ∇·J_I − κ ∇·J_S + β P requires dimensional consistency across all
terms. Let [C] = C (coherence density), [t] = T (time), [x] = L (length), [J] = C/T (density per unit time). Then: •
∂C/∂t: [C]/[T] = C/T ✓ • ∇·J_C: [J_C]/[L] = (C/T)/L = C/(TL) ... Wait, this suggests J_C should have spatial
divergence units. Let me reconsider. Correct interpretation: J_C is coherence flux (coherence per unit time per
unit area), so [J_C] = C/(T·L²). Then ∇·J_C = (1/L) · (C/TL²) = C/(TL³), which doesn't match ∂C/∂t = C/T unless
we work in dimensionless or per-volume form. Proper formulation: Work with densities per unit volume. Then
∂C/∂t has units [coherence density]/[time]. ∇·J_C has units [flux]/[length] = [coherence density per unit
time]/[length] · [1/length] = [coherence density]/[time] ✓. Full dimensional analysis with nondimensionalization,
stability analysis, and limiting-case checks is provided in the full manuscript's Section C.2. Here, the key point is
that all terms must be expressed in units of [coherence density per unit time] for the equation to be consistent.
Appendix C: Key References and Directions for Further Study
This framework draws on and extends ideas from: 1. Non-equilibrium Thermodynamics and Transport
Equations: Evans, D.J., Searles, D.J. (2002). The fluctuation theorem. Advances in Physics, 51(7),
1529–1585. — Foundational work on transport laws and continuity equations. 2. Open Quantum Systems and
Decoherence: Breuer, H.-P., Petruccione, F. (2002). The Theory of Open Quantum Systems. Oxford
University Press. — Standard reference for Lindblad equations and coherence decay. 3. Phase Synchrony
and Communication Through Coherence in Neural Systems: Fries, P. (2015). Rhythms for cognition:
communication through coherence. Neuron, 88(1), 220–235. — Empirical foundation for coherence-based
neural communication. 4. Order Parameters and Phase Transitions: Landau, L.D., Lifshitz, E.M. (1980).
Statistical Physics (3rd ed.). Pergamon Press. — Theoretical framework for coherence as an order parameter.
5. Active Matter and Non-Equilibrium Dynamics: Marchetti, M.C., et al. (2013). Hydrodynamics of soft active
matter. Reviews of Modern Physics, 85(3), 1143. — Context for coherence as a transported/organized quantity
in driven systems. 6. Quantum Feedback Control: Wiseman, H.M., Milburn, G.J. (2009). Quantum
Measurement and Control. Cambridge University Press. — Theoretical basis for coherence stabilization
through feedback. Future theoretical work should address: • Nonlinear stability analysis of the continuity
equation under various boundary conditions. • Coupling to thermal reservoirs and detailed balance conditions. •
Numerical simulations of toy models on various network topologies. • Formal reduction from microscopic
Hamiltonian dynamics to coarse-grained continuity form. Future experimental work should address: • Design
and implementation of high-fidelity quantum optics and interferometric tests (Section 6.1, 6.2). • Extraction of
coherence flux measurements from neural recordings with sufficient temporal and spatial resolution. •
Collaborative efforts with condensed-matter groups to implement proposals in Section 6.3.