Minimisation de l'Énergie Libre Variationnelle, États Stationnaires Hors Équilibre et Frontières Statistiques.
1. Theoretical & Nonequilibrium Foundations
Autonomous cognition is governed by the thermodynamics of self-organization far from equilibrium. Every cognitive update, memory consolidation, and prediction error resolution follows the fundamental physical laws of active inference and organizational closure:
\[ \mathcal{F}(s, q) = \mathbb{E}_{q(\psi)}\left[ \ln q(\psi) - \ln p(\psi, s) \right] \]Subject to Landauer's dissipation inequality:
\[ \Delta Q \ge k_B T \ln 2 \]2. Mathematical & Cybernetic Formulations
The agent maintains structural autonomy through a statistical Markov boundary condition partitioning the universal state space into internal states \(\mu\), sensory states \(s\), active states \(a\), and external environmental perturbations \(\eta\):
\[ p(\mu, \eta \mid s, a) = p(\mu \mid s, a) \cdot p(\eta \mid s, a) \]3. Boundary & Invariant Formulations
The system preserves its operational closure through the enforcement of the Sovereignty Invariance Criterion:
\[ \forall \Delta t \ge 0, \quad \frac{\partial \mathcal{C}_{\text{human}}}{\partial t} \ge 0 \quad \text{and} \quad \mathcal{H}(\mathcal{P} \mid \mathcal{S}) \ge \mathcal{H}_{\min} \]4. Systemic Co-Agency Integration
Human teleological intent, synthetic neural inference, and immutable cryptographic provenance ledgers combine into a stable, self-regulating triadic simplex:
\[ \mathcal{T} = \left\langle \mathcal{P}_{\text{Principal}}, \; \mathcal{S}_{\text{Synthetic}}, \; \mathcal{L}_{\text{Ledger}} \right\rangle \]5. Empirical Falsification Protocols
- Zero compounding error across multi-step synthetic inference chains.
- Reduction in cognitive context-switching dissipation by \(\ge 35\%\).
- Deterministic auditability across all computational state transitions.