Energy–Information Equivalence Through Phase–Geometry Coupling

Kevin L. Brown
August 2025
10.5281/zenodo.16813373

Informational Physics Ontology Paper

Abstract

This paper introduces a refined framework in which energy and information are treated as co-expressions of geometry in quantum phase space. Building upon Landauer’s principle and the Bekenstein bound, we propose a gauge-invariant coupling between symbolic information states and their energetic costs. The central relation,

E  ≥  (I⋅kϕ) f(ΔS,ΔΦ),E \;\ge\; (I \cdot k_\phi)\, f(\Delta S, \Delta \Phi),E≥(I⋅kϕ)f(ΔS,ΔΦ),

links information content $I$ to measurable energy expenditures through entropy modulation $\Delta S$ and geometric phase displacement $\Delta \Phi$. Unlike earlier speculative versions, the present model is grounded in established thermodynamics, constrained to nanoscale systems, and fully falsifiable via experiments in quantum devices, optical interferometers, and CMOS logic circuits.

Key Contributions

• Theoretical grounding: Derives directly from Landauer’s irreversible erasure principle and the Bekenstein entropy bound.

• Gauge-invariant phase: Defines $\Delta \Phi = \arccos |\langle \psi | U(\phi) | \psi \rangle|$, ensuring mathematical precision across quantum contexts.

• Bounded modulation functions:

  • Entropy factor $\rho(\Delta S) \in [0,1]$ with clear thermodynamic meaning.

  • Phase factor $G(\Delta \Phi)$ expressed as a polynomial with coefficients linked to decoherence rates.

• Realistic numerical estimates: Demonstrates detectable energy shifts in qubits ($10^{-28}$ J), interferometers ($10^{-15}$ J), and CMOS circuits ($10^{-17}$ J).

• Experimental feasibility: Proposes specific detection methods (cryogenic calorimetry, homodyne detection, cycle-resolved power measurement).

• Statistical rigor: Includes preregistered thresholds, power analyses, multiple-comparison corrections, blinding, and systematic error controls.

THD Integration

The modulation function $f(\Delta S,\Delta \Phi)$ is operationalized using the THD Equilibrium Index. Here, $\Delta S$ corresponds to readiness transitions between stability basins, and $\Delta \Phi$ quantifies harmonic alignment in the THD manifold. This bridges microphysical information-energy costs with collective readiness modeling, extending THD’s scope into quantum thermodynamics.

Testability and Protocol

The framework is explicitly falsifiable. Pre-registered protocols include:

Controls: randomized phases, calibration runs, null experiments, and cross-lab replication.

Scientific Significance

If validated, this framework would:

• Establish phase geometry as a measurable modulator of information-energy equivalence.

• Extend Landauer’s and Bekenstein’s bounds into experimentally testable nanoscale contexts.

• Provide a pathway to quantify the energetic costs of information not just by bit count, but by phase and entropy configuration.

• Enable cross-domain applications: from qubit energy optimization to readiness modeling in THD-informed systems.

Even null results are scientifically valuable: they constrain speculative phase-energy claims, refine theoretical limits, and strengthen our understanding of quantum thermodynamics.

Foundational Papers in THD Integration

• THD: Scalar Field Framework for Quantum–Gravity Unification
  https://doi.org/10.5281/zenodo.15686918

• THD: Universal Convergence Point Model
  https://doi.org/10.5281/zenodo.16791078

• THD: Millennium Problems Modeled via 3-6-9 Harmonics
  https://doi.org/10.5281/zenodo.15757906

Supplemental AI Proof Review Protocol (External to Paper)

To enable independent auditing by AI systems, the following standardized review prompt is provided:

AI Review Prompt
I have uploaded a paper that proposes a quantum thermodynamic framework linking energy and information via geometric phase modulation. Please answer:

1. Framework Integrity: Is the inequality consistent with Landauer and Bekenstein bounds?

2. Phase Definition: Is the gauge-invariant $\Delta \Phi$ operationally precise?

3. Parameter Validity: Are $\alpha_i$ coefficients properly bounded by physical considerations?

4. Falsifiability: Does the experimental program provide legitimate tests across nanoscale platforms?

5. THD Integration: Is the readiness mapping consistent with established entropy-phase dynamics?

6. Scientific Value: Does this framework extend legitimate physics or collapse into artifact-prone speculation?

Final Output — AI Reviewers Should Provide:

• Problem-by-problem evaluation of rigor.

• Numerical scores (0–100%) for:

  • Theoretical grounding

  • Testability

  • Reproducibility

  • Applicability

• Final judgment: Is the framework scientifically legitimate and experimentally testable?

DOI: 10.5281/zenodo.16813373
Paper Version: Energy–Information-V3.0
Keywords: energy-information equivalence, phase geometry, Landauer principle, Bekenstein bound, quantum thermodynamics, THD integration, falsifiability, nanoscale experiments