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RFT as a Cross-Domain Organizing Principle: Analogies to Thermodynamics and Information Theory

Clinton Svancara

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This note clarifies the conceptual role of Relational Field Theory (RFT) and positions it as a cross-domain organizing principle rather than a domain-specific model or a replacement for existing physical theories. RFT introduces a minimal structure: a coherence field R_cgoverned by a persistence law, and an adaptive domain closure that makes memory state-dependent. From this minimal structure, the framework reproduces recurring dynamical signatures across multiple regimes, including: spontaneous threshold crossing, critical slowing, hysteresis, coherence wells, and persistent structured correlations under noise. The purpose of this paper is to show that RFT functions in a role analogous to thermodynamics or information theory: it does not replace the underlying dynamical laws of a system, it constrains the conditions under which coherence and temporal order can emerge within those dynamics, and it remains substrate-independent, with different domains corresponding to different projections of the same underlying structure. To illustrate this organizing role, the paper includes a numerical demonstration of coherence revival in a strongly driven open quantum system using the RFT adaptive kernel. This simulation is not presented as proof of the effect, but as a minimal demonstration that the framework generates the predicted qualitative behavior. A reproducible Python implementation is included in the appendix. This framing helps distinguish RFT from a constructed metric or simulation-specific method. Instead, it supports the interpretation of RFT as a structural constraint on persistence-driven coherence across classical, quantum, and complex systems.

DOI
10.17605/osf.io/pwdfs

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This note clarifies the conceptual role of Relational Field Theory (RFT) and positions it as a cross-domain organizing principle rather than a domain-specific model or a replacement for existing physical theories. RFT introduces a minimal structure: a coherence field R_cgoverned by a persistence law, and an adaptive domain closure that makes memory state-dependent. From this minimal structure, the framework reproduces recurring dynamical signatures across multiple regimes, including: spontaneous threshold crossing, critical slowing, hysteresis, coherence wells, and persistent structured correlations under noise. The purpose of this paper is to show that RFT functions in a role analogous to thermodynamics or information theory: it does not replace the underlying dynamical laws of a system, it constrains the conditions under which coherence and temporal order can emerge within those dynamics, and it remains substrate-independent, with different domains corresponding to different projections of the same underlying structure. To illustrate this organizing role, the paper includes a numerical demonstration of coherence revival in a strongly driven open quantum system using the RFT adaptive kernel. This simulation is not presented as proof of the effect, but as a minimal demonstration that the framework generates the predicted qualitative behavior. A reproducible Python implementation is included in the appendix. This framing helps distinguish RFT from a constructed metric or simulation-specific method. Instead, it supports the interpretation of RFT as a structural constraint on persistence-driven coherence across classical, quantum, and complex systems.
This note presents a concrete, falsifiable prediction of Relational Field Theory (RFT) in a regime where standard open-system quantum treatments provide well-defined expectations. Consider a strongly driven open quantum system (e.g., superconducting qubit arrays or cavity-QED platforms) subject to dissipation. Under standard Lindblad or Floquet descriptions, such systems are typically expected to exhibit monotonic coherence decay or steady-state saturation without a revival mechanism of this form. RFT predicts a different outcome. Due to the adaptive domain closure T[R_c], the system’s effective response time increases in the low-coherence regime. This allows accumulated relational structure to persist long enough for the system to spontaneously re-enter a high-coherence state. The result is a non-monotonic coherence revival that arises without fine-tuning or additional parameters. Observable signatures include: Non-monotonic coherence lifetime (decay → plateau → revival) Hysteresis under drive-amplitude cycling Divergence of recovery time near a critical drive strength (critical slowing) A sharp increase in the time-quality factor Q_t=1/D_\theta The key discriminating feature is the combined appearance of these signatures. While individual behaviors may appear in nonlinear or driven systems, their joint occurrence under these conditions is not naturally predicted by standard open-system models. This prediction provides a direct experimental test of RFT. If high-precision measurements in the specified regime show only monotonic decay with no revival or hysteresis, the adaptive-closure mechanism of RFT would be ruled out. This work does not modify quantum mechanics. Instead, it proposes that coherence-constrained dynamics arising from relational persistence may constitute a cross-domain organizing structure that can be tested within existing experimental platforms.
This project presents a clarification of earlier Relational Field Theory (RFT) work on quantum tunneling, measurement, and relational quantum gravity through the lens of recent regime-dependent coherence results. The paper argues that structure-sensitive coherence should not be interpreted as a globally active mechanism. Instead, it becomes dynamically relevant only under conditions of strong local closure, recoverability, and persistent boundary-constrained organization. The note introduces: • regime-dependent activation of structural coherence, • a closure functional for relational domains, • recoverability as a condition for persistent organization, • linearized perturbation decay inside deep-well regimes, • and stable macroscopic records as outcome-defining degrees of freedom. This framing connects recent turbulence-based computational evidence to quantum-foundations questions without claiming a universal solution to the measurement problem. It positions earlier RFT quantum papers as architectural sketches now constrained by local validity, regime dependence, and computational results.
This paper derives the core structure of Relational Field Theory (RFT) from a minimal set of constraints, showing that the multiplicative coherence functional ( R_c = \alpha \cdot \beta \cdot \gamma ) and the linear persistence law ( \frac{dR_c}{dt} = -\lambda R_c + F_{int} ) emerge naturally rather than being arbitrarily chosen. The derivation is based on four principles: collapse invariance, relational closure, measurability, and stability. It demonstrates that alternative functional forms either violate these constraints or fail to reproduce the observed phenomenology, including persistence, critical slowing, hysteresis, and coherence wells. Up to monotonic transformations and scaling, the resulting structure represents the minimal continuous and invariant form consistent with the constraints. This work provides a foundational justification for the RFT framework and clarifies why its core formulation arises as the simplest structure that satisfies both physical and operational requirements.
This paper presents the application of Relational Field Theory (RFT) to random circuit sampling (RCS), a standard benchmark in quantum computing. Building on the reduced relational law: {\dot{R}}_c=-\lambda R_c+F_{int},\bigm and the operational coherence functional: R_c=\alpha\cdot\beta\cdot\gamma,\bigm the framework is applied to reported RCS data from superconducting qubit experiments. Within this setting: α corresponds to distribution sharpness (e.g., cross-entropy benchmark or peak statistics) β reflects circuit connectivity and gate structure γ captures persistence across circuit depth and repeated runs Using published results, the relational coherence functional is evaluated against observed behaviors in RCS systems, including: Persistence of structured output distributions beyond expected circuit depth Formation of coherence wells, where structure remains stable under noise Attractor-like clustering of high-probability output states Suppression of entropy relative to fully randomized expectations These observations are consistent with the four falsifiable predictions introduced in RFT v2.0: critical slowing near coherence thresholds hysteresis-like behavior under parameter variation persistence in coherence wells emergence of structural anchors This work does not modify quantum mechanics or attempt to reproduce standard RCS results. Instead, it provides a structural interpretation of observed behavior using a coherence-based framework applied to existing experimental data. The results extend Relational Field Theory from classical and toy-model systems into the quantum domain, supporting its potential as a cross-domain framework for understanding persistence, structure, and transition dynamics.
This note uses results from anisotropic turbulent channel flow to clarify the interpretive scope of earlier quantum papers in the Relational Field Theory (RFT) series. Structure-sensitive coherence is shown to activate conditionally in boundary-constrained regimes, supporting a regime-dependent view of coherence-driven mechanisms. Earlier explorations of quantum tunneling, measurement, and relational quantum gravity are best understood as processes that become dynamically relevant only under conditions of strong local closure and persistent relational structure. The framing maintains scientific modesty while providing a methodological constraint for quantum applications of RFT.
This document presents the formal mathematical axiomization of Relational Field Theory (RFT), establishing a single ontological primitive— the bounded scalar coherence field —and deriving the self-referential domain constraint .The Axiom Sheet (A1–A9) formalizes the Kernel identity, coherence evolution equation, domain threshold conditions, Genesis principle, and measurement-as-locking interpretation. A second section provides representative derived theorems showing how known physical laws emerge as limiting behaviors of and , including: Schrödinger equation as phase-locked Kernel dynamics Newtonian mechanics as low-curvature Rc trajectories General relativity as effective curvature geometry of Rc Maxwell/gauge structure as coherence-preserving invariants Thermodynamics as entropy of coherence loss Absence of physical singularities from Rc-threshold constraints This document serves as the foundational formal layer for the full RFT corpus, establishing the axiomatic base from which all subsequent proofs and derivations follow.