Entropy Dissipation and Informational Collapse in the Collatz Process

We present a novel informational reformulation of the Collatz process based on binary structure and entropy dynamics. Rather than analyzing numerical trajectories arithmetically, we study the propagation of bitwise information across iterations of the transformation x \mapsto \frac{3x+1}{2} and the subsequent halving steps. Our key insight lies in the structural asymmetry of the process: informational growth is strictly bounded — each application of 3x+1 adds at most two new bits — while informational collapse, induced by cascading carry operations and division by two, is unbounded and statistically more probable. Residual bits generated during iteration exhibit localized, self-reabsorbing behavior, leading to entropy dissipation rather than accumulation. We argue that the Collatz trajectory, viewed as a logical automaton over bitstrings, does not possess the informational degrees of freedom required to diverge. This informational asymmetry, combined with the non-invertibility of the transformation, strongly supports convergence as a structural inevitability. While this work does not constitute a classical proof, it establishes the foundations for an entropic theory of convergence and invites further formalization of non-numeric invariants in recursive systems. The Collatz transformation is not strictly a mathematical function, but a rule-based bitwise system. Therefore, its convergence behavior must be studied in terms of logical propagation, not algebraic invariants.