arXiv:2512.17961v1 Announce Type: new
Abstract: We propose that spacetime dynamics can be organized by a Planck-scale bookkeeping rule, applied per modular $2 pi$ interval, that balances the geometric entropy increment $delta A/4G$ against a reversible modular-energy flow $delta langle Krangle$ and an irreversible Landauer-Bennett cost $ln 2 delta N_c$, 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 $N_c$ 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 $rho_{vac} = rho_{Lambda} + 3 varepsilon H^2 / 8 pi G$ when a constant inefficiency parameter epsilon is assumed.