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.