Callan-Symanzik-like equation in information theory (2508.13330v1)

Abstract: In this paper, we consider the jumps in the complexity growth rate (CGR) through the complexity=anything proposal. It is revealed that bulk fields are in charge of the height and the location of these jumps. To put it accurately, their counterparts are divergence of energy momentum tensor, shear viscosity and the Weyl anomaly of the boundary theory. The behavior of CGR around these jumps manifests a critical behavior and critical exponents. Moreover, it is figured out that CGR satisfies a Callan-Symanzik-like equation around these jumps. This equation suggests that the speed of information processing could be changed by the scale of energy. Put it another way, by change of the scale of energy one could turn the classical computers into faster processor computers even faster than our current quantum computers.