Measure-Theoretic Diagnostics of Architectural Entanglement in Asymmetric Multiprocessing Systems: A Boltzmann Uniqueness Approach

Orchestration of Asymmetric Multiprocessing Platforms (AMPs), such as ARM big.LITTLE, frequently relies on the heuristic assumption of cluster independence, wherein high-performance (“Big”) and high-efficiency (“Little”) cores operate as computationally orthogonal resources. These cores are partitioned into “islands” of separate power/performance clusters, operating on independent/voltage frequency rails. However, these platforms share resources, including Last-Level Cache (LLC), main memory, and interconnects across all cores. Therefore, we assume that islands interact, operating in a functionally “coupled state.” To conduct a measure-theoretic evaluation of this assumption, we apply the Boltzmann uniqueness theorem, recently demonstrated to be the singular method to determine the veracity of this assumption. Mathematically, we define an “uncoupled” system as one whose joint resource measurement is strictly the convolution of its subsystem measures. We evaluate two distinct AMP topologies—Orange Pi 5 and Cubie A7A under controlled saturation—and demonstrate a systemic failure of convolution commutativity. We subsequently expand this investigation to high-performance x86 hybrid architectures via the Intel i7-12800H platform. Our findings, characterized by significant negative power correlations and the failure of predictive convolution models, constitute a counterexample for cluster independence. We identify shared architectural resources, specifically the LLC and shared power rails, as the likely physical mechanisms of “architectural entanglement,” rendering traditional additive performance models underspecified.