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arXiv 2408.11279gr-qcastro-ph.COhep-ph
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平坦FLRW宇宙学中耗散与非耗散宇宙的全息热力学关系

Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology

Nobuyoshi Komatsu

AI总结:

本研究在平坦FLRW宇宙中,利用贝肯斯坦-霍金熵和Kodama-Hayward温度,推导了耗散与非耗散宇宙的修正全息热力学关系,并探讨了其与标准第一定律的等价性及热力学量演化。

摘要:

为阐明一种全息修正热力学关系,本研究将平坦FLRW宇宙中宇宙学方程的一般表述应用于热力学第一定律,采用贝肯斯坦-霍金熵$S_{\rm{BH}}$和动态Kodama-Hayward温度$T_{\rm{KH}}$。对于一般表述,现象学上假设了耗散宇宙(如体粘滞宇宙学)中宇宙流体的有效压力$p_{e}$,以及非耗散宇宙(如时变$\Lambda(t)$宇宙学)中的额外驱动项$f_\Lambda(t)$。当$f_\Lambda(t)$为常数时,修正热力学关系等价于标准宇宙学中第一定律的表述。该修正关系的一侧描述体中的热力学量,可分解为两个时间导数项,即$\dot\rho$项和$\dot{V}$项,其中$\rho$为宇宙流体的质量密度,$V$为哈勃体积。利用吉本斯-霍金温度$T_{\rm{GH}}$,该关系的另一侧$T_{\rm{KH}} \dot{S}_{\rm{BH}}$可表述为$T_{\rm{GH}} \dot{S}_{\rm{BH}}$与$[(T_{\rm{KH}}/T_{\rm{GH}}) -1] T_{\rm{GH}} \dot{S}_{\rm{BH}}$之和,这两项分别等价于$\dot\rho$项和$\dot{V}$项,其中$\dot{V}$项的大小与$\dot\rho$项的平方成正比。此外,通过应用视界上的能量均分定律,检验了常数$f_\Lambda(t)$情况下的修正热力学关系。当考虑常数$T_{\rm{KH}}$宇宙时,该修正热力学关系归结为一种扩展的全息类连接。本文还利用常数$T_{\rm{KH}}$模型讨论了热力学量的演化,扩展了先前分析[Phys. Rev. D 108, 083515 (2023) (arXiv:2306.11285)]。

英文摘要:

To clarify a holographic modified thermodynamic relation, the present study applies a general formulation for cosmological equations in a flat FLRW universe to the first law of thermodynamics, using the Bekenstein-Hawking entropy $S_{\rm{BH}}$ and a dynamical Kodama-Hayward temperature $T_{\rm{KH}}$. For the general formulation, both an effective pressure $p_{e}$ of cosmological fluids for dissipative universes (e.g., bulk viscous cosmology) and an extra driving term $f_Λ(t)$ for non-dissipative universes (e.g., time-varying $Λ(t)$ cosmology) are phenomenologically assumed. When $f_Λ(t)$ is constant, the modified thermodynamic relation is equivalent to the formulation of the first law in standard cosmology. One side of this modified relation describes thermodynamic quantities in the bulk and can be divided into two time-derivative terms, namely $\dotρ$ and $\dot{V}$ terms, where $ρ$ is the mass density of cosmological fluids and $V$ is the Hubble volume. Using the Gibbons-Hawking temperature $T_{\rm{GH}}$, the other side of this relation, $T_{\rm{KH}} \dot{S}_{\rm{BH}}$, can be formulated as the sum of $T_{\rm{GH}} \dot{S}_{\rm{BH}}$ and $[(T_{\rm{KH}}/T_{\rm{GH}}) -1] T_{\rm{GH}} \dot{S}_{\rm{BH}}$, which are equivalent to the $\dotρ$ and $\dot{V}$ terms, respectively, with the magnitude of the $\dot{V}$ term being proportional to the square of the $\dotρ$ term. In addition, the modified thermodynamic relation for constant $f_Λ(t)$ is examined by applying the equipartition law of energy on the horizon. This modified thermodynamic relation reduces to a kind of extended holographic-like connection when a constant $T_{\rm{KH}}$ universe is considered. The evolution of thermodynamic quantities is also discussed, using a constant $T_{\rm{KH}}$ model, extending a previous analysis [Phys. Rev. D 108, 083515 (2023) (arXiv:2306.11285)].

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