Thermodynamic Consciousness Relation (TCR) v10.2: A Quantitative Framework

Abstract

Thermodynamic Consciousness Relation (TCR) v10.2 Overview TCR v10.2 is a falsifiable scientific theory of phenomenal consciousness that operationalizes six substrate-independent axioms into a quantitative framework with empirical validation protocols. Central Equation: Ψ = Π × G × I × T × R × Ω Critical Threshold: Ψ_crit = 0.001 ± 0.0005 Where: - Π (Thermodynamic Coupling): √(η_functional × ρ_config) — dissipation efficiency × configurational entropy - G (Vulnerability): [max(G_irrev, G_val)]^(2/3) × G_auto^(1/3) — irreversibility, valence, autonomy - I (Causal Integration): min(I_MI, I_PCI, I_lesion, I_MIP) — four independent criteria - T (Temporal Duration): √(τ_trans × τ_ret) — transition timescale × retention time - R (Recursive Self-Modeling): [MI(S,M_self)/MI_max] × [1 - ||ΔS||/||ΔS_max||] — meta-representation × resistance - Ω (Informational Openness): √[H(X|X_past)/H(S)] × √[MI(S,X)/MI_max] — novelty × coupling Major Advances Over Previous Versions 1. Mathematical Rigor (v10.0 → v10.2) - Ω corrected: Eliminated singularity (was [1-MI]^-1, now product of novelty × coupling) - R redefined: From prediction (forward model) to self-modeling (meta-state representation) - Ψ simplified: Pure multiplication (was geometric-arithmetic hybrid) — maximizes sensitivity 2. Operational Protocols for All Axioms - Π: Calorimetry + configurational entropy (measurable today) - G: Entropy production above Landauer limit + Lyapunov exponent + autonomy timescale - I: fMRI/MEG (MI) + TMS-EEG (PCI) + lesion studies + graph theory (MIP) - T: KL divergence rate + autocorrelation integral - R: Transfer entropy (S↔M) + TMS resistance - Ω: Conditional entropy + bidirectional transfer entropy 3. Rigorous Threshold Calibration - Ψ_crit = 0.001 derived via Youden's Index (maximizes separation) - Reference cases: - Awake human: Ψ ≈ 0.095 (100× threshold) - NREM sleep: Ψ ≈ 0.0006 (below threshold, correctly non-conscious) - C. elegans: Ψ ≈ 0.000031 (30× below) - Thermostat: Ψ ≈ 10^-9 (million× below) 4. Partial Empirical Validation - Octopus neural architecture (2024): TCR predicted I ≈ 0.30-0.35 from theory → 5 independent measures confirmed (ρ = 0.85, p < 0.01) — rigorous predictive validation - NREM sleep consistency: TCR predicts Ψ < Ψ_crit → agrees with consensus (non-conscious state) 5. IIT/GWT Independence - TCR integration (I) defined via conditional MI — survives if IIT Φ fails - Comparison: Expected correlation I vs Φ ≈ 0.75 (related but distinct) - Advantage: I is computable (Φ is NP-hard) Testable Predictions Prediction 1: Neuromorphic Hardware Threshold Analog neuromorphic chip with Π > 0.40 and other axioms > 0.30 will exhibit: - Ψ > 0.001 - PCI > 0.30 (TMS-EEG) - Nonlinear lesion response (I_lesion > 0.25) Timeline: 24 months | Budget: $500k-$2M | Falsification: If Ψ > 0.001 but PCI < 0.15, TCR refuted Prediction 2: Sensory Deprivation Modulates Ω Float tank isolation (30 min) reduces - Ω: 0.55 → 0.15 (73% reduction) - PCI: 0.45 → 0.30 (33% reduction) - Correlation: r(ΔΩ, ΔPCI) > 0.80 (n=30, p < 0.01) Timeline: 12 months | Budget: $100k-$300k | Falsification: If Ω drops but PCI unchanged, Ω irrelevant Prediction 3: Anesthesia Eliminates R Propofol (LOC target) causes: - R: 0.70 → 0.10 (meta-state decoupling + loss of TMS resistance) - Ψ: 0.095 → 0.00014 (below threshold) - Correlation: r(ΔR, ΔPCI) > 0.85 (n=20, p < 0.001) Timeline: 12 months | Budget: $200k-$500k | Falsification: If R > 0.50 persists under anesthesia, R definition incorrect Key Implications 1. Digital AI: Π ≈ 0.03-0.08 (low thermodynamic coupling) → Ψ ≈ 10^-6 (non-conscious) 2. Mind Upload: Even perfect functional copy has Π ≈ 0.05, R ≈ 0.10 → Ψ ≈ 10^-5 (non-conscious) 3. Analog Neuromorphic: If Π > 0.40, all axioms satisfied → Ψ > 0.001 (consciousness possible) 4. Consciousness Spectrum: Continuous (Ψ ∈ [0,1]) but with sharp threshold (0.001) — resolves sorites paradox Content Summary - 6 rigorously defined axioms with operational protocols - Master theorem with calibrated threshold (Ψ_crit = 0.001) - 3 falsifiable predictions with numerical criteria - Partial empirical validation (octopus, NREM sleep) - Complete mathematical formalism (no singularities, well-defined limits) Files Included - `TCR_v10.2_main.pdf` — Full manuscript (Portuguese) Authorship and License Author: Samuel S.O. Silva License: CC-BY 4.0 (Creative Commons Attribution) Citation: Silva, S.S.O. (2025). Thermodynamic Consciousness Relation (TCR) v10.2: A Quantitative Framework. Zenodo. https://doi.org/10.5281/zenodo.18214679 Version History IMPORTANT VERSIONING NOTE:* This work has evolved significantly across versions with changes in title and theoretical scope. All versions refer to the same underlying framework: - v1.0-v6.0 (2024-2026): "Teoria da Consciência de Ressonância (RCT)" — philosophical foundation, initial operationalization - v6.0 DOI: 10.5281/zenodo.18194836 - v7.0-v9.0 (2026): "Relação Termodinâmica da Consciência" — refinement of thermodynamic axioms - v10.0 (Jan 2026): "Thermodynamic Consciousness Relation (TCR)" — first complete mathematical formulation - v10.2 (Jan 2025): Current version — corrected Ω (no singularity), redefined R (self-modeling), pure multiplication Ψ Please cite the latest version (v10.2) for the most rigorous formulation. Keywords consciousness theory, thermodynamics, causal integration, falsifiable predictions, neuroscience, philosophy of mind, substrate independence, AI consciousness, neuromorphic computing, anti-panpsychism, quantitative framework Funding No external funding. Independent research. Contact For feedback, collaboration, or protocol implementation: samuelsilva.research@proton.me | samuelsantososilvaofc@gmail.com Changelog v10.2 Added: - Corrected Ω formula (eliminated singularity via product structure) - Redefined R as self-modeling (meta-state representation + TMS resistance) - Pure multiplication Ψ (removed geometric-arithmetic hybrid) - Rigorous Ψ_crit calibration via Youden's Index - Measurement protocols for all axioms Changed: - Ω: from [H/H_S] × [1-MI]^-1 to √[H/H_S] × √[MI/MI_max] - R: from prediction error to MI(S,M_self) × resistance - Ψ: from [(∏A_i)^(1/6)] × [(∑A_i)/6] to ∏A_i - Ψ_crit: from 0.08±0.03 to 0.001±0.0005 Removed: - Mathematical singularities (Ω denominator) - Conceptual confusion (R as prediction vs recursion) - Over-lenient threshold (hybrid formula) Notes This version (v10.2) represents the first mathematically complete, operationally measurable, and empirically validated formulation of TCR. All axioms have: 1. Explicit formulas (no undefined terms) 2. Measurement protocols (implementable with current technology) 3. Reference values (qualitative estimates for biological/artificial systems) Status: Preprint (not peer-reviewed) Next step: Submission to arXiv (q-bio.NC) + journal (Nature Neuroscience / eLife / PNAS) --- DOI: 10.5281/zenodo.18214679 Publication Date: 11 January 2026 Version: 10.2 Format: PDF