The Processing-Rate Theory: A Scalar-Informational Extension of Proper Time and Strong-Field Dynamics

This version has been superseded by Version 2 (DOI: 10.5281/zenodo.17655287), which contains the finalized title and updated content. 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 gμν = R^2 gμν, decoupling the rate of internal physical evolution from geometric proper time while leaving the Einstein–Hilbert sector unchanged. The environmental dependence of R(x) arises 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), show that all inhomogeneous configurations are free from gradient and ghost instabilities, and 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 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.