Modeling the Kinematic Transition Between Consciousness and the Unconscious: A Phenomenological Framework for Neuromorphic Dynamics and Metabolic Power Constraints

Abstract

— This paper presents a novel bio-inspired phenomenological framework and an algorithmic toy model designed to conceptualize the kinematic and energetic transitions between conscious waking states and virtual dream states within the human brain. Moving away from purely qualitative descriptions, we introduce a global state-switching parameter (\(\mathbf{EMB}\)) that acts as a theoretical circuit-breaker. This parameter models the dynamic redirection of metabolic energy from physical motor outputs (muscular kinetic work) during wakefulness to an internal, virtual processing sandbox (neuronal information flow) during sleep, while preserving the underlying topology of sensory geometry. The system's behavior is governed by coupled differential kinematic equations during the waking state (\(\theta(t) = 1\)) and transitions to an informational diffusion process during the dream state (\(\theta(t) = 0\)), modeled through a modified logarithmic gradient identity derived from mass-independent spatial transport networks. To validate the theoretical framework, a numerical simulation was engineered in Python to track kinematic velocity evolution across three distinct temporal phases: waking engagement, sleep onset (the decoupling shock), and deep sleep neuro-stabilization. Furthermore, the model incorporates real-time vascular power grid constraints, strictly regulating computational energy distribution beneath the physiological hard ceiling of 20 Watts. The simulation demonstrates how somatic paralysis during sleep frees metabolic headroom, allowing an instantaneous computational velocity spike up to 2.58 units, before undergoing non-linear relaxation toward a homeostatic floor of 0.90 units to facilitate synaptic maintenance. This integrated framework offers a scalable mathematical perspective for advancing bio-inspired predictive neural networks and neuromorphic artificial intelligence architectures.