A Unified RECT Interpretation of Quantum Entanglement, Quantum Transitions, Black Holes, and the Cosmic Heat-Death Cycle: A Mathematical Framework Based on Referential Structures, Energy-Potential Differences, and Entropy

This paper presents a unified interpretation within Referential Entropy Cycle Theory (RECT) of quantum entanglement, quantum transitions, black holes, and the cosmic heat-death cycle. RECT treats physical quantities as quantitative expressions of referential relations. Energy-potential difference is a central physical variable: relative energy-potential differences characterize distinctions between reference structures, while absolute energy-potential difference describes the global state relevant to cosmic evolution. Entropy characterizes the informational state of referential configurations and is related to the evolution of energy-potential differences. Within this framework, quantum entanglement is interpreted in terms of shared referential information and common phase selection. Quantum transitions are treated as discrete changes in referential structure that may involve mass-energy conversion. Black holes are interpreted as regions containing nested phase-transition structures, while cosmic heat death and phase reset are considered stages in a proposed cyclic model of cosmic evolution. The paper connects these phenomena through a common theoretical framework based on referential structures, energy-potential differences, entropy, and state transitions. The proposed interpretations are presented as part of RECT and are distinguished from completed quantitative derivations or empirical confirmation.