Callan-Symanzik-like equation in information theory
Quantum Physics
2026-05-29 v3 High Energy Physics - Theory
Abstract
Within the "complexity=anything" proposal of holography, the complexity growth rate (CGR) can exhibit jumps, interpreted as phase transitions. We demonstrate that the location and amplitude of these jumps are governed by the dynamics of bulk fields, which, via the fluid-gravity correspondence, map to the boundary energy-momentum tensor. The behavior of the CGR near these critical points exhibits scaling and universality. We show that the CGR satisfies a Callan-Symanzik-like equation near the transitions. Our results provide a new information-theoretic interpretation of the Callan-Symanzik equation, with the CGR running with the energy scale.
Cite
@article{arxiv.2508.13330,
title = {Callan-Symanzik-like equation in information theory},
author = {Mojtaba Shahbazi and Mehdi Sadeghi},
journal= {arXiv preprint arXiv:2508.13330},
year = {2026}
}
Comments
16 pages, two figures, Minor modifications made