发表机构
Universidad del Atlántico（大西洋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究指数型f(Q)引力模型的表观视界热力学，推导熵微分修正贝肯斯坦-霍金面积定律，利用GSL判据约束参数空间，发现b的观测拟合值满足GSL而过大的b会违反GSL。
AI 中文摘要
我们在空间平坦的弗里德曼-勒梅特-罗伯逊-沃尔克背景和重合规范下，研究了以参数b和n为特征的指数型f(Q)引力模型中表观视界的热力学。针对n=1的解，我们采用哈勃参数的近似宇宙学解（指数参数b的二阶近似），研究了表观视界半径和Kodama-Hayward温度的红移演化。我们根据Misner-Sharp-Hernandez质量、功密度和能量供给矢量构建了Hayward统一第一定律，并证明视界动力学可获得平衡态热力学描述。相关熵微分与$f_Q+2Qf_{QQ}$成正比，对贝肯斯坦-霍金面积定律产生指数抑制的修正，且在$b\to0$的极限下回归$S=A/4$。随后我们通过纳入表观视界内物质的熵来检验广义第二定律（GSL），当物质温度与视界温度相等时，我们采用文献中先前推导的GSL可行性判据$f_Q+2Qf_{QQ}\u22650$。观测驱动的b最佳拟合值在研究的红移区间内满足该条件，且主要在晚时表现出与$\u039b$CDM模型的偏离；相反，足够大的正值（约$b>0.26$）会在未来区域$z<0$中违反GSL。这些结果表明，表观视界热力学为指数型f(Q)宇宙学的参数空间提供了互补约束。
英文摘要
We investigate the thermodynamics of the apparent horizon in an exponential $f(Q)$ gravity model characterized by the two parameters $b$ and $n$, within a spatially flat Friedmann--Lemaître--Robertson--Walker background and the coincident gauge. Focusing on the $n=1$ solution, we use the approximate cosmological solution for the Hubble parameter up to second order in the exponential parameter $b$ to study the redshift evolution of the apparent-horizon radius and the Kodama--Hayward temperature. We formulate Hayward's unified first law in terms of the Misner--Sharp--Hernandez mass, the work density, and the energy-supply vector, and show that the horizon dynamics admits an equilibrium thermodynamic description. The associated entropy differential is proportional to $f_Q+2Qf_{QQ}$, yielding exponentially suppressed corrections to the Bekenstein--Hawking area law and recovering $S=A/4$ in the limit $b\to0$. We then examine the generalized second law (GSL) by including the entropy of matter inside the apparent horizon. When the matter and horizon temperatures are identified, we adopt the GSL viability criterion $f_Q+2Qf_{QQ}\geq0$ previously derived in the literature. The observationally motivated best-fit values of $b$ satisfy this condition over the redshift interval studied and produce departures from $Λ$CDM mainly at late times. In contrast, sufficiently large positive values, approximately $b>0.26$, can violate the GSL in the future region $z<0$. These results show that apparent-horizon thermodynamics provides a complementary constraint on the parameter space of exponential $f(Q)$ cosmology.
Comments22 pages, 5 figures. References added. Submitted to Int. J. Mod. Phys. D
