Spacetime Dynamics and Local Entropy Balance on Causal Horizons

TL;DR

This work proposes that spacetime dynamics are governed by an information-geometry ledger that balances the geometric entropy increment on causal screens with reversible modular-energy flow and irreversible Landauer costs. Grounded in the entanglement first law and the Bekenstein–Hawking entropy, the ledger recovers the nonlinear Einstein equations in the small-ball limit and naturally yields a two-component running vacuum in FLRW with a constant inefficiency parameter $\varepsilon$. A key result is that the cosmological vacuum density takes the form $\rho_{vac}=\rho_\Lambda+\frac{3\varepsilon H^2}{8\pi G}$, where $\varepsilon$ encodes horizon information-processing irreversibility. The framework offers an information-theoretic foundation for gravity, suggesting laboratory tests of entanglement thermodynamics and precision cosmology to constrain $\varepsilon$, and points to extensions to far-from-equilibrium dynamics relevant for black-hole and early-universe phenomena.

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 $ρ_{vac} = ρ_Λ + 3 \varepsilon H^2 / 8 πG$ when a constant inefficiency parameter epsilon is assumed.