Thermodynamic Criticality in FLRW Cosmology with Non-extensive Loop Quantum Gravity Entropy
Abstract
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→1, the critical point is continuously pushed to vc→∞ and Tc→0. 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 (αcr,βcr,γcr,δcr) =(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 RN∼−|v−vc|−4 on the critical isotherm, and RN∼−|t|−2 on the critical isochore. Finally, the critical expansion scale is given by Hc2=2(√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.
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BibTeX
@misc{cruz2026thermodynamic,
title = {{Thermodynamic Criticality in FLRW Cosmology with Non-extensive Loop Quantum Gravity Entropy}},
author = {Miguel Cruz and Joel Saavedra and Juan Rodriguez},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27721},
eprint = {2608.27721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27721},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Thermodynamic Criticality in FLRW Cosmology with Non-extensive Loop Quantum Gravity Entropy
AU - Miguel Cruz
AU - Joel Saavedra
AU - Juan Rodriguez
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27721
UR - https://arxiv.org/abs/2608.27721
AB - 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→1, the critical point is continuously pushed to v_c→∞ and T_c→0. 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∼−|v−v_c|^−4 on the critical isotherm, and R_N∼−|t|^−2 on the critical isochore. Finally, the critical expansion scale is given by H_c^2=2(√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.
ER -