2025/12/18 by Song, Daegene
#FOS: Physical sciences #General Physics (physics.gen-ph)
paper · doi:10.48550/arxiv.2512.17961
We propose that spacetime dynamics can be organized by a Planck-scale bookkeeping rule, applied per modular 2 π interval, that balances the geometric entropy increment δA/4G against a reversible modular-energy flow δ⟨ K⟩ and an irreversible Landauer-Bennett cost ln 2 δNc, where K is the (dimensionless) modular Hamiltonian of the chosen region defined relative to the chosen reference state, generating entanglement flow across the local screen and Nc counts logically irreversible classical record updates (registration strokes) on that screen. This "information-geometry ledger" is consistent with the Bekenstein-Hawking area law, and -- when enforced on small causal screens under the standard entanglement-equilibrium assumptions -- recovers the full nonlinear Einstein equation. In FLRW cosmology, the same bookkeeping motivates a two-component vacuum sector ρvac = ρΛ + 3 ε H2 / 8 πG when a constant inefficiency parameter epsilon is assumed.