Information Thermodynamics in the Tenson Framework: Entropy Production and the Arrow of Time

The origin of temporal irreversibility remains a central problem in the foundations of physics. While microscopic dynamical laws are typically time-reversal invariant, macroscopic phenomena exhibit a pronounced arrow of time, conventionally captured by the second law of thermody- namics. The present paper addresses this tension within the Tenson framework, which treats energy and information as coupled physical quantities. Building on the structural incompleteness of the Tenson field and its quantum extension, we show that entropy production arises as a necessary consequence of irreducible residual structure. Rather than postulating irreversibility as a statistical tendency or boundary condition, we derive it from the interplay of energy–information exchange, quantization, and coarse-grained temporal synchronization. We introduce the notion of Tenson entropy as a measure of structural openness and demon- strate that monotonic entropy increase follows without additional axioms. Within this approach, the arrow of time emerges as a structural feature of the theory rather than an externally imposed principle. Connections to classical thermodynamics are discussed, while broader cosmological and biological implications are left for future work.