The Thermodynamic Debt Shifting Paradox: Systemic Reflection and Topological Reconstruction at the Physical Limits of Semiconductor Scaling

This paper develops a statistical-physics framework for the thermodynamic debt shifted from operational energy reduction in advanced semiconductor systems to manufacturing, packaging, and infrastructure-scale entropy generation. The contributions of this study are threefold. First, it formalizes the energy consumption of the semiconductor scaling trajectory into an asymmetric entropy debt decomposition, strictly distinguishing between operational entropy generation (ΔSoperation) and manufacturing entropy generation (ΔSmanufacturing). Second, based on the Gouy-Stodola theorem, it establishes a conditional analysis of debt conservation across the manufacturing-operation boundary and formally defines the Thermodynamic Debt Shifting Paradox. The research demonstrates that within traditional three-dimensional physical space and von Neumann architectures, any local operational power-reduction effort is rigidly shifted and amplified into hidden entropy debt at the manufacturing and infrastructure levels, leading to conditional physical infeasibility. Third, to overcome this rigid thermodynamic boundary, the study proposes Topological Geometric Offload, leveraging the optimal high-dimensional packing symmetry of the 24-dimensional Leech lattice (Λ24) and dynamic perturbation rectification based on non-equilibrium stochastic resonance as a dimensional-shift paradigm and future research direction for prototype validation. This framework also provides a common physical foundation for the AGI physical-layer analysis developed in the companion paper The Causal Vacuum of Digital Fingerprints: A Physical-Layer Thermodynamic Framework for AGI-Scale Forgery Analysis.