NESSField + SheathWorld: A Non-Equilibrium Developmental Cognitive Architecture

NESSField+SheathWorld proposes a developmental cognitive architecture grounded in non-equilibrium statistical physics and the Free Energy Principle (FEP). The core theoretical contribution is a formal correspondence between classical PID control and the Fokker-Planck decomposition of non-equilibrium steady states (NESS): the proportional and derivative terms shape the Wang potential landscape, while the integral term generates and maintains the probability curl that sustains NESS. Based on this correspondence, the paper derives a meta-control loop for managing I-term momentum, a correspondence between precision adaptation in FEP and adaptive PID gain scheduling, and a mapping of seven metacognitive components to control-theoretic primitives. A corrected subgraph isomorphism bound for structure generalization is derived and numerically validated on NESSField-scale feature graphs. Keywords: free energy principle, PID control, non-equilibrium steady state, cognitive architecture, developmental robotics