Time Reversal, Entropy Relativity, and Computational Naturalness: A Unified Perspective on the Arrow of Time

We investigate the fundamental nature of \emph{time‑reversal symmetry} and its progressive breakdown in complex, structured dynamical systems. Drawing on the fluctuation theorem and recent quantum time‑reversal experiments, we show that although microscopic laws remain reversible, the emergence of \emph{computational naturalness}, characterized by a compact \emph{calculation cone} for forward prediction and an expansive \emph{retrodiction sphere} for reversal, inevitably yields intrinsic irreversibility. We formalize this via the \emph{naturalness ratio}, comparing the informational requirements of reversal versus prediction, and demonstrate how structural complexity and causal constraints sharply curtail the duration of reversible dynamics. Concurrently, we introduce a formal measure of \emph{entropy relativity}: an \emph{observer‑relative entropy} based on a Kullback–Leibler divergence that reproduces Gibbs entropy in equilibrium while capturing nonlocal correlations. Applied to cosmology, entropy relativity reveals that the early Universe, maximally entropic in its co‑moving frame, appears low in entropy when measured against its later expanded state, resolving the low‑entropy initial condition puzzle. We classify systems into \emph{fully reversible}, \emph{entropy‑resistant}, and \emph{structurally irreversible} regimes, and examine the role of \emph{CPT symmetry} in preserving fundamental laws despite quantum‑level asymmetries. Together, these insights bridge microscopic reversibility and macroscopic irreversibility, offering a \emph{unified framework} for entropy relativity, computational naturalness, and the cosmological arrow of time.