An Effective Framework for Entropy Modifications via Stochastic Metric Fluctuations
arXiv:2602.16294 · doi:10.1016/j.aop.2026.170685
Abstract
Deviations from the area law of horizon entropy are often modeled phenomenologically through modified Friedmann equations in cosmology. In this work, we explore an effective stochastic interpretation of such modifications by considering a Friedmann--Robertson--Walker (FRW) universe perturbed by a conformal, time-dependent noise factor with vanishing mean. Averaging the Einstein equations to second order in the fluctuation amplitude yields an effective correction to the Friedmann equation. We show that, in the spatially flat case with vanishing cosmological constant, this correction can be effectively matched to the general form induced by a deformed entropy-area relation. Within this phenomenological framework, the noise variance can be suitably chosen to match the functional forms associated with several generalized entropy models, including Renyi, (dual) Kaniadakis, Barrow, logarithmic, and MOND-inspired hypergeometric entropies. The present analysis therefore provides an effective correspondence between stochastic metric fluctuations and entropy deformations.
v2: 11 pages, 1 table. Clarifications added; results unchanged. Accepted for publication in Annals of Physics