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.
Probing the Holographic Universe: Aspects of Entanglement Entropy Modifications
Universidad Andrés Bello（安德烈斯贝洛大学）；Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Universidad de Tarapacá（塔拉帕卡大学）；Charles University（查理大学）；Pontificia Universidad Católica de Valparaíso（瓦尔帕莱索天主教 Pontificia 大学）
