The Embodied Computation Trilemma: Thermodynamic Boundaries, Phase-Space Collapse, and Deterministic Control in Vision-Language-Action Models

Contemporary physical artificial intelligence (Physical AI) and vision-language-action (VLA) foundation models rest upon an unproven foundational axiom: that dynamic interaction within continuous physical space-time can be asymptotically resolved by scaling discrete floating-point operations (FLOPs) and multimodal autoregressive tokens. In this work, we formalize the fundamental limits of this paradigm as The Embodied Computation Trilemma, establishing a rigorous mathematical and thermodynamic bound connecting control efficiency (E), hardware/compute cost (C), and physical safety bounds (S): E · S/C ≤ kembodied Grounded in micro-scale Landauer dissipation and macro-scale second-law thermodynamic constraints, we prove that unconstrained optimization toward maximizing efficiency (E → 1) while stripping away physical safety margins (S → 0) inevitably induces Phase-Space Divergence and Material Constitutive Inadmissibility when confronting discontinuous contact boundaries and friction bifurcations in the real world. To resolve this epistemic deadlock, we introduce a deterministic, zero-heap C99 fault-tolerant state estimator as a zero-stack safety layer, ensuring bounded momentum reacquisition for hard real-time embedded systems. This work bridges abstract algorithmic assets with physical reality, backed by our comprehensive 20-part Physical Intelligence (PI) matrix.