Spacetime Dynamics and Local Entropy Balance on Causal Horizons

TL;DR

This paper introduces a Planck-scale bookkeeping rule that links spacetime geometry, entropy, and information flow, recovering Einstein's equations and suggesting a two-component vacuum model in cosmology.

Contribution

It proposes a novel information-geometry ledger framework that unifies spacetime dynamics with entropy and information flow, consistent with the area law and Einstein equations.

Findings

Recovers Einstein's equations from entropy and information flow principles.

Proposes a two-component vacuum energy model in FLRW cosmology.

Aligns with the Bekenstein-Hawking area law.

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.