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具有对数修正的FRW宇宙学的广义热力学第二定律

Generalized second law of thermodynamics for FRW cosmology with logarithmic correction

H. Mohseni Sadjadi, Mubasher Jamil

备注：
14 pages, accepted for publication in Europhysics Letters
发表信息：
EPL, 92 (2010) 69001
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摘要：

在以前的文献中关于加速膨胀宇宙中广义第二定律（GSL）的分析中，通常的熵面积关系，即$S={A\over 4G}$，被用于宇宙学视界熵。但这种熵关系可能由于热和量子涨落或由圈量子引力激发的修正而被修改，从而产生S ={A \over 4}+ π α \ln（{A \over 4}）+ γ，其中$α$和$γ$是一些常数，其值在文献中仍有争议。我们的目的是研究GSL对这些参数的约束。此外，我们还通过对广义相对论的有效性的要求，研究了熵中修正项的存在对系统的其他物理参数如暗能量温度的影响。在我们的研究中，我们考虑一个空间平坦的Friedman-Robertson-Walker，并假设宇宙是由几个相互作用的组件（包括暗能量）。该模型的背景下，热平衡和非平衡的情况下进行了研究。我们表明，在（超）加速宇宙GSL是有效的，每当$α(<)>0$导致一个（负）正的贡献，从对数修正的熵。在超加速的情况下，暗能量的温度小于或等于霍金温度。

英文摘要：

In the previous analyses in the literature about the generalized second law (GSL) in an accelerated expanding universe the usual area relation for the entropy, i.e. $S={A\over 4G}$, was used for the cosmological horizon entropy. But this entropy relation may be modified due to thermal and quantum fluctuations or corrections motivated by loop quantum gravity giving rise to S={A\over 4}+πα\ln({A\over 4})+γ, where $α$ and $γ$ are some constants whose the values are still in debate in the literature. Our aim is to study the constraints that GSL puts on these parameters. Besides, we investigate the conditions that the presence of such modified terms in the entropy puts on other physical parameters the system such as the temperature of dark energy via requiring the validity of GSL. In our study we consider a spatially flat Friedman-Robertson-Walker and assume that the universe is composed of several interacting components (including dark energy). The model is investigated in the context of thermal equilibrium and non-equilibrium situations. We show that in a (super) accelerated universe GSL is valid whenever $α(<)>0$ leading to a (negative) positive contribution from logarithmic correction to the entropy. In the case of super acceleration the temperature of the dark energy is obtained to be less or equal to the Hawking temperature.

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