THE ARROW OF TIME AS INFORMATION ERASURE IN A FINITE-CAPACITY UNIVERSE

The physical origin of the arrow of time remains a foundational problem: microscopic laws are largely time-reversal invariant, yet macroscopic evolution is irreversible. This work advances a structural account rooted in the physicality of information and finite informational capacity. Let a bounded physical region (or any operationally closed subsystem) have a finite maximum information capacity (in bits), consistent with Bekenstein and holographic bounds. We show that any sustained sequential physical evolution that continually instantiates new distinguishable states within this finite capacity must reuse degrees of freedom, which generically requires logically irreversible operations—i.e., overwrite/erasure in the operational sense of making prior microstate information thermodynamically inaccessible—unless an ever-growing external memory is available. Using Landauer’s principle, erasure of bits implies a minimum entropy export and heat dissipation . We formalize an erasure-budget inequality linking cumulative forward-time entropy production to the minimal information that must be overwritten to sustain ongoing state replacement under finite capacity, and then strengthen it into a strong-form capacity–erasure theorem that yields explicit lower bounds: sustained novelty plus finite capacity forces compulsory overwrite and thus compulsory entropy production. We further formulate a quantum strong form using mutual information monotonicity under CPTP maps (data processing inequality), identifying the arrow of time as the direction of monotone decrease of accessible past information. Optionally, we show that applying holographic horizon capacity and the Gibbons–Hawking temperature yields the natural cosmological energy-density scale , providing a quantitative consistency check. The analysis introduces no new dynamical laws; it isolates boundary/consistency conditions that any coherent ontology of time must satisfy in a finite-capacity physical universe.