Adaptive Collapse Dynamics

Abstract: This paper introduces a fundamentally new conceptual approach to systemic degradation: Adaptive Collapse Theory. Shifting the paradigm from traditional viewing of entropy and chaos as blind, stochastic forces, we demonstrate that the destruction of both informational and material structures follows a strictly deterministic trajectory that can be mathematically predicted. By expanding the classical phase space and introducing a fundamental hidden stability parameter L(t), which represents the internal adaptive resource or structural density of an object, the work formalizes systemic failure as a consequence of free-energy minimization in the extended state space. To bridge the gap between high-level physics and practical understanding, the paper provides an intuitive real-world baseline analogy of battery capacity degradation under environmental loads, followed by a rigorous, internally closed mathematical apparatus. The proposed framework removes major ad hoc assumptions of previous phenomenological data degradation models, shifting the study of entropy from philosophical speculation into the domain of predictive engineering. This theory provides the core mathematical skeleton for practical applications in computational systems, including dynamic Large Language Model (LLM) KV-cache management (ACE) and Linux page replacement policies.