具有非广延圈量子引力熵的FLRW宇宙学中的热力学临界性
Thermodynamic Criticality in FLRW Cosmology with Non-extensive Loop Quantum Gravity Entropy
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中文总结 AI 辅助
该研究探讨具有非广延圈量子引力熵的FLRW宇宙学的热力学临界性，推导修正弗里德曼动力学与视界状态方程，发现临界点特性、临界指数及曲率标度，建立自洽临界结构并保留平均场普适性。
中文摘要 AI 辅助
我们研究空间平坦的弗里德曼-勒梅特-罗伯逊-沃尔克（FLRW）宇宙在其表观视界上具有非广延圈量子引力启发熵时的热力学临界性。利用完整的Kodama-Hayward温度和统一第一定律，我们推导了修正的弗里德曼动力学并构建了相应的视界状态方程。我们发现有限物理临界点仅出现在非广延分支q>1，而在贝肯斯坦-霍金极限q→1下，临界点会连续推移至v_c→∞且T_c→0。沿同一旋节线，定压热容和等温压缩率均变为无界，该曲线的极值位于临界点。低于临界温度时，吉布斯自由能形成多个热力学分支，不同视界状态的相共存通过温度、压力和吉布斯自由能的相等性得到验证。临界指数为(α_cr,β_cr,γ_cr,δ_cr)=(0,1/2,1,3)，表明尽管状态方程为非代数形式，该系统仍属于标准平均场普适类。归一化Ruppeiner曲率恰好沿旋节线发散，在临界等温线上呈现临界标度R_N∼-|v-v_c|^{-4}，在临界等容线上呈现R_N∼-|t|^{-2}。最后，临界膨胀标度由H_c²=2(√5-2)|β|给出，这意味着当熵变形为1阶时，热力学临界点出现。这些结果为宇宙表观视界的有效热力学状态空间建立了自洽的临界结构，并保留了平均场临界普适性。
英文摘要
We investigate thermodynamic criticality in a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker universe with a non-extensive Loop Quantum Gravity inspired entropy on its apparent horizon. Using the full Kodama-Hayward temperature and the unified first law, we derive the modified Friedmann dynamics and construct the corresponding horizon equation of state. We see that a finite physical critical point only appears in the non-extensive branch $q>1$, while in the Bekenstein-Hawking limit $q\to1$, the critical point is continuously pushed to $v_c\to\infty$ and $T_c\to0$. Along the same spinodal curve, both the constant-pressure heat capacity and the isothermal compressibility become unbounded, and the extremum of this curve is located at the critical point. Below the critical temperature, the Gibbs free energy develops several thermodynamic branches, and the phase coexistence for different horizon states is verified by the equality of temperature, pressure, and Gibbs free energy. The critical exponents are $(α_{cr},β_{cr},γ_{cr},δ_{cr}) =(0,1/2,1,3)$, indicating that the system belongs to the standard mean-field universality class despite the non-algebraic form of the equation of state. The normalized Ruppeiner curvature diverges precisely on the spinodal curve and shows critical scaling $R_N\sim-|v-v_c|^{-4}$ on the critical isotherm, and $R_N\sim-|t|^{-2}$ on the critical isochore. Finally, the critical expansion scale is given by $H_c^2=2(\sqrt{5}-2)|β|$, which implies that the thermodynamic critical point occurs when the entropy deformation is of order unity. These results establish a self-consistent critical structure for the effective thermodynamic state space of the cosmological apparent horizon and retain the mean-field critical universality.
