Reversible Quantum Control Is Not Time Reversal: Unitary Undoing vs. Irreversible Erasure and a Unified Taxonomy of Temporal Arrows

We present a unified operational framework for the arrow of time grounded in irreversible information loss. While microscopic physical laws are time-reversal invariant, macroscopic irreversibility arises when systems overwrite metastable records. We show that recent reversible quantum-control experiments do not reverse time, but instead operate in regimes where no logically irreversible record is created. To formalize this, we introduce the **forgetting rate** \ ( (₂ₑ) \), a coarse-grained rate defined on physically selected metastable record states (e. g. , pointer states, memory registers, or macroscopic configurations). Unlike standard entropy production, which is expressed in terms of microscopic transition asymmetry, \ ( (₂ₑ) \) captures the **rate of irreversible record overwriting**. In this formulation, entropy production obeys the lower bounḋ₈ₑₑ kB \, ₂ₑ, with Landauer's principle but expressed at the level of record dynamics. Within this framework, thermodynamic, quantum-measurement, psychological, and cosmological arrows emerge as substrate-dependent manifestations of \ (₂ₑ > 0\). Temporal asymmetry is therefore not a single global property, but a distributed feature of physical information-processing systems. The approach naturally explains the decoupling of arrows in composite systems and identifies experimentally accessible regimes where irreversibility can be locally suppressed. This work does not introduce a new microscopic law but provides a unifying, operational reformulation that connects information thermodynamics, decoherence theory, and memory dynamics through a single coarse-grained rate.