The Processing-Rate Theory: Physical Time as Local State-Evolution Rate in Relativistic Spacetimes

This work develops the Processing-Rate Theory (PRT), a scalar-informational extension of general relativity in which physical proper time is governed by a local processing-rate field R (x). Matter evolves according to an effective temporal metric g̃⏛⏜ = R² g⏛⏜, decoupling the rate of internal physical evolution from geometric proper time while leaving the Einstein–Hilbert sector unchanged. The environmental dependence of R (x) is introduced through a Landau-type potential V (R, ρ, S) sensitive to local energy and entropy densities, providing a unified informational account of time dilation in high-density and high-entropy regimes. We analyze the dynamical stability of R (x), demonstrating that all inhomogeneous configurations are free from gradient and ghost instabilities, and we derive observational predictions including entropy-dependent gravitational redshift, modified collapse timescales, and deviations in the evolution of neutron-star merger remnants. In gravitational collapse, R (x) naturally forms a zero-processing core, halting internal physical evolution without altering the external GR geometry and offering a non-singular resolution of classical black-hole interiors. The Processing-Rate Theory provides a consistent and testable framework linking relativity, thermodynamics, and quantum information. It preserves the empirical successes of general relativity while opening new avenues for observational and theoretical investigation in extreme astrophysical environments.