Spacetime Dynamics and Local Entropy Balance on Causal Horizons

Abstract: 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 $δ\langle K\rangle$ and an irreversible Landauer-Bennett cost $\ln 2 δN_c$, 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 $ρ{vac} = ρΛ + 3 \varepsilon H^2 / 8 πG$ when a constant inefficiency parameter epsilon is assumed.