Microscopic Unitarity and the Quantization of Black Hole Evaporation Time

TL;DR

This paper develops a microscopic, unitary quantum model for black hole evaporation, using a bipartite subsystem approach and a capacity constraint to explain entropy dynamics and information preservation.

Contribution

It introduces a novel microscopic Hamiltonian framework with a capacity constraint to ensure unitarity and explain the entropy turnaround in black hole evaporation.

Findings

Explicit unitary evolution of radiation during evaporation

Derivation of a quantum condition linking microscopic phases and macroscopic entropy

Natural explanation of entropy turnaround and final state purification

Abstract

This work presents an effective microscopic, time-dependent Hamiltonian framework for investigating information dynamics during black hole evaporation. While current approaches often rely on gravitational path integrals or statistical ensembles to recover the Page curve, our model provides an explicit, unitary quantum-mechanical evolution of the radiation. We utilize the Independent Unitary Pairing assumption, where the total Hilbert space is decomposed into N_{total} mutually independent bipartite subsystems. Each subsystem consists of a single interior qubit interacting unitarily with a single radiation qubit, ensuring strict global microscopic unitarity (Von Neumann entropy =0) throughout the process. To reconcile this with macroscopic thermodynamics, we introduce a methodology called "Fermion-like Occupancy Bound", which can be considered as a Holographic Binary Capacity Constraint, where each radiation channel is modeled as a two-level system representing the fundamental unit of information. This truncation, justified by the holographic principle at the Planck scale, enforces a maximum entropy bound of ln2 per channel, which naturally yields the entropy turnaround and final state purification. The central result of this framework is the derivation of a Quantum Condition for Unitarity , which couples microscopic phase evolution with macroscopic observables.