Spacetime Dynamics and Local Entropy Balance on Causal Horizons

Abstract

We propose that spacetime dynamics can be organized by a Planck-scale bookkeeping rule, written using a modular-parameter normalization of size $2\pi$, that balances the geometric entropy increment $\delta A/4G$ against a reversible modular-energy flow $\delta\!\langle K\rangle$ and an irreversible Landauer--Bennett cost $\ln 2\,\delta N_c$, where $K\equiv K_\sigma$ is the (dimensionless) modular Hamiltonian of the chosen region defined relative to a fixed reference state $\sigma$, and $N_c$ counts logically irreversible one-bit record updates (e.g. coarse-grained overwrites or 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 $\rho_{\rm vac}=\rho_\Lambda+3\varepsilon H^{2}/8\pi G$ when a constant inefficiency parameter $\varepsilon$ is assumed.