Spacetime dynamics and local entropy balance on causal horizons

We propose that spacetime dynamics can be organized by a Planck-scale bookkeeping rule, written using a modular-parameter normalization of size Formula: see text, that balances the geometric entropy increment Formula: see text against a reversible modular-energy flow Formula: see text and an irreversible Landauer–Bennett cost Formula: see text, where Formula: see text is the (dimensionless) modular Hamiltonian of the chosen region defined relative to a fixed reference state Formula: see text, and Formula: see text counts logically irreversible one-bit record updates (e.g. coarse-grained overwrites/registrations) 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 Formula: see text when a constant inefficiency parameter Formula: see text is assumed.