Arrow of Time from Finite Geometric Relaxation

The origin of the cosmological arrow of time remains unresolved, as the fundamental equations governing gravity and spacetime dynamics are largely invariant under time reversal. In this work, we propose an interpretational framework in which a macroscopic arrow of time emerges naturally from the finite relaxation dynamics of spacetime geometry itself. Within the context of Finite-Relaxation Geometry (FRG), spacetime is treated as a non-equilibrium system characterized by a finite geometric relaxation time, allowing it to retain long-lived memory of past curvature perturbations. We argue that the irreversible dissipation of this geometric memory provides a natural, non-entropic origin of temporal asymmetry, independent of special initial conditions or modifications of the Einstein field equations. The resulting geometric arrow of time is shown to be conceptually consistent with previously discussed halo phenomenology in FRG and with large-scale cosmological evolution, including effects commonly attributed to dark energy. Crucially, the framework remains empirically accountable: finite relaxation implies history-dependent and temporally nonlocal gravitational responses, leading to clear falsifiability criteria at astrophysical and cosmological scales. FRG thus offers a minimal and testable perspective on the emergence of time asymmetry grounded in non-equilibrium spacetime geometry.