NESSField+SheathWorld: A Developmental Cognitive Architecture from Non-Equilibrium Statistical Physics

We present NESSField+SheathWorld, a developmental cognitive architecture grounded in non-equilibrium statistical physics. We establish a formal correspondence between PID control and the Fokker-Planck decomposition of non-equilibrium steady states (NESS), confirmed by independent derivation in the active inference literature. Single-particle experiments validate that FEP gradient descent produces cognitively meaningful behaviors (perception tracking, object permanence) while inevitably reaching thermal death; a multi-particle basin birth-death framework is proposed as theoretical resolution. The PID-FPE correspondence is numerically validated in 1D/2D; single-particle cognitive behaviors are experimentally confirmed; system-level emergence remains future work. This work was developed with AI-assisted literature review, mathematical proof verification, and LaTeX typesetting; all theoretical contributions, experimental design, and final decisions remain solely the author’s own. Keywords: Free Energy Principle, PID Control, Non-Equilibrium Steady State, Cognitive Architecture, Developmental Robotics