Irreversibility as Informational Closure: A Structural Account of Temporal Direction

The direction of time is typically explained through entropy increase, special boundary conditions (Past Hypothesis), or coarse-grained statistical asymmetries. While these approaches successfully account for macroscopic irreversibility, they often presuppose entropic structure rather than isolating the minimal dynamical condition under which temporal asymmetry arises. This paper proposes a structural account of irreversibility grounded in the contraction of forward-accessible state sets under deterministic dynamics. Given a measurable state space (X,T), we define forward accessibility relative to an initial state and introduce a normalized Accessibility Loss Index (ALI) that quantifies monotonic contraction of dynamically reachable states. We prove a minimal forward-contraction theorem showing that structural irreversibility emerges under absorbing or forward-invariant subsets, independently of entropy, coarse-graining, or boundary-condition assumptions. The resulting framework does not compete with entropy-based accounts but clarifies a more primitive structural condition: temporal direction corresponds to measurable contraction in accessibility under forward dynamics. Irreversibility is thus characterized as informational closure intrinsic to state-space structure rather than as an epistemic artifact. The paper situates this account relative to entropy-based, Past Hypothesis, and asymptotic explanations, arguing that accessibility contraction provides a formally minimal and ontologically explicit condition for temporal asymmetry