Non-extensive Tsallis thermostatistics is a widespread paradigm to describe large-scale gravitational systems. In this work we use Tsallis Cosmology to study thermodynamic gravity and derive modified Friedmann equations. We show that corrections induced by non-extensivity affect the Hubble function evolution during the radiation-dominated epoch. In turn, this leads to non-trivial modifications of the mass density and pressure content of the Universe, which provide a viable mechanism allowing for baryogenesis, even in the presence of the standard interaction between the Ricci scalar and baryon current. By demanding consistency with current observational bounds on baryogenesis, we constrain Tsallis δ parameter to be $|\delta -1|\simeq {10}^{-3}$. Based on the recently established connection between Tsallis thermostatistics and the quantum gravitational generalization of the uncertainty principle at Planck scale (GUP), we finally show that this bound is in agreement with the estimation of the GUP parameter predicted by many quantum gravity models.

非扩展 Tsallis 恒温是描述大规模引力系统的广泛范式。在这项工作中，我们使用 Tsallis Cosmology 来研究热力学引力并推导出修正的弗里德曼方程。我们表明，非广延性引起的修正会影响辐射主导时期的哈勃函数演化。反过来，这会导致宇宙的质量密度和压力含量发生重大变化，这为重子生成提供了可行的机制，即使在里奇标量和重子流之间存在标准相互作用的情况下也是如此。通过要求与当前对重粒发生的观察范围保持一致，我们将 Tsallis δ参数限制为$|\delta -1|\simeq {10}^{-3}$. 基于最近建立的 Tsallis 恒温学与普朗克尺度（GUP）不确定性原理的量子引力泛化之间的联系，我们最终表明该界限与许多量子引力模型预测的 GUP 参数的估计一致。