We investigate the fundamental nature of 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 are reversible, the emergence of computational structures that locally resist entropy production inevitably leads to intrinsic irreversibility. To quantify this phenomenon, we introduce the concept of \emph{time-entropy momentum}, a measure integrating local entropy production and entropy flux divergence, characterizing a system’s inherent resistance to entropy increase. We demonstrate that structural complexity, combined with high time-entropy momentum, imposes a robust upper bound on the duration over which reversible dynamics can persist before irreversibility dominates. Concurrently, we reexamine conventional notions of entropy from a relational perspective. Within this framework, the early Universe, though maximally entropic within its co-moving reference frame, appears low in entropy when viewed from its later expanded configuration. This reinterpretation offers new insight into the longstanding cosmological puzzle of the Universe's low-entropy initial conditions. We classify physical, biological, and computational systems into distinct regimes: fully reversible, entropy-resistant, and structurally irreversible. Additionally, we explore the implications of CPT symmetry, illustrating how full CPT conjugation preserves fundamental physical laws despite quantum-level asymmetries. Collectively, we propose that these insights bridge microscopic reversibility and macroscopic irreversibility, offering a unified framework for understanding the interplay among entropy dynamics, computational evolution, and the cosmological arrow of time.