Emergent Temporal Compatibility in Unitary Dynamics

Abstract We investigate the emergence of an operational temporal limit for coherent recombination in globally unitary quantum dynamics. Using numerical interferometric simulations, we introduce an operational notion of temporal compatibility defined through the decay of interferometric visibility, without invoking wavefunction collapse, classical noise, or external dissipation. Through systematic numerical simulations of a minimal unitary model with a finite internal sector, explicitly formulated in interferometric terms, we show that temporal compatibility exhibits qualitatively distinct dynamical regimes. In systems with low spectral density, coherence losses are transient and compatibility remains recoverable through spontaneous revivals. By contrast, when temporal incompatibility is distributed across an internal sector with sufficiently dense spectral structure, the visibility decays without relevant revivals, and a well-defined compatibility timescale, Δτcompat, becomes operationally accessible. We demonstrate that this emergent timescale is statistically robust, invariant under changes in microscopic clock dynamics, and controlled by collective spectral properties rather than by subsystem-specific parameters. In the post-compatibility regime, Δτcompat obeys a simple scaling law governed by an effective collective parameter combining coupling strength and spectral dispersion. These results provide a concrete mechanism for the emergence of operational irreversibility within globally unitary systems and establish temporal compatibility as a meaningful dynamical notion. More broadly, they support interpretations in which effective temporal horizons arise from internal dynamical structure rather than from fundamental state reduction or observer-dependent processes.