Communicability Exponent as a Differential Scaling Index of the Graph Family G(s)
Year: 2026
Type: article
Abstract: In previous works it was shown that the phenomenological law N ∼ sD successfullydescribes the hierarchy of interactions. In the present note this law receives a mathematicallywell-defined formulation. We introduce the differential communicability exponentDc(s) = d lnN/d ln s as a characteristic of the scale flow of graphs G(s). It is provedthat if communicability is covariant under coarse-graining, then Dc(s) is constant. Arelation between the differential exponent and the effective index D(s) is established:Dc(s) = D(s) + ln s · dD/d ln s. Effective estimates of Dc(s) are obtained from data on44 systems. A systematic variation is found: from ∼ 0.90 for electromagnetic systems to∼ 1.03 for nuclear ones. This indicates near scale invariance of the vacuum graph andturns Dc(s) into a characteristic of its scale regime amenable to independent verification.
Author: Gromov, Alexey
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202139392