The recent research on the connection between gravity and thermodynamics suggests that gravity could be an emergent phenomenon. Following this, Padmanabhan proposed a novel idea that the expansion of the universe can be interpreted as equivalent to the emergence of space with the progress of cosmic time. In this approach, the expansion of the universe is described by what is known as the law of emergence, which states that the expansion of the universe is driven by the difference between the number of bulk and surface degrees of freedom in a region bounded by the Hubble radius. This principle correctly reproduces the standard evolution of a Friedmann universe. We establish the connection of the law of emergence, which is conceptually different from the conventional paradigm to describe cosmology, with other well-established results in thermodynamics. It has been shown that the law of emergence can be derived from the unified first law of thermodynamics, which can then be considered as the backbone of the law. However, the law of emergence is rich in structure than implied by the First law thermodynamics alone. It further explains the evolution of the universe towards a state of maximum horizon entropy. Following this, it can be considered that the first law of thermodynamics, along with the additional constraints imposed by the maximisation of the horizon entropy, can together lead to the law of emergence. In the present article, we first make a brief review of Padmanabhan’s proposal and then studies its connection with the thermodynamics of the horizon in the context of Einstein’s, Gauss-Bonnet, and more general Lovelock gravity theories.

最近关于重力和热力学之间联系的研究表明，重力可能是一种新兴现象。此后，帕德马纳班提出了一个新颖的观点，即宇宙的膨胀可以解释为随着宇宙时间的进展而出现的空间。在这种方法中，宇宙的膨胀由所谓的涌现定律描述，该定律指出，宇宙的膨胀是由一个区域的体积自由度和表面自由度之间的差异驱动的哈勃半径。这个原理正确地再现了弗里德曼宇宙的标准演化。我们建立了出现规律的联系，这在概念上不同于描述宇宙学的常规范式，与热力学中其他公认的结果。已经表明，涌现定律可以从统一的热力学第一定律推导出来，然后可以将其视为该定律的支柱。然而，涌现定律的结构比热力学第一定律单独暗示的要丰富。它进一步解释了宇宙向最大视界熵状态的演化。在此之后，可以认为热力学第一定律，连同视界熵最大化所施加的额外约束，可以共同导致涌现定律。在本文中，我们首先简要回顾 Padmanabhan 的提议，然后在爱因斯坦、Gauss-Bonnet 和更一般的 Lovelock 引力理论的背景下研究它与视界热力学的联系。