发表机构
National Observatory of Athens; University of Science and Technology of China; Universidad Católica del Norte; University of Lleida; University of Patras; Perimeter Institute for Theoretical Physics; University of Waterloo（雅典国家天文台; 中国科学技术大学; 北方天主教大学; 莱里达大学; 帕特雷大学; 理论物理前沿研究所; 滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本综述统一阐述熵在引力与宇宙学中的作用，涵盖黑洞热力学、全息原理、时空热力学猜想、全息暗能量及熵引力，旨在厘清熵的角色并指出未来研究方向。
AI 中文摘要
熵已成为引力、量子理论与宇宙学交叉领域中的关键概念，揭示了几何、信息与热力学之间的深层联系。黑洞是热力学系统这一认识——其特征是熵与其视界面积成正比——为时空本身可能具有微观结构提供了证据。此后，熵在量子场论、全息原理、量子引力及宇宙学中获得了核心地位。在本综述中，我们对引力与宇宙学语境下的熵给出了统一阐述。我们首先考察引力系统中的熵，重点关注黑洞热力学、熵界、全息原理、纠缠熵及面积定律，并讨论由量子场论、广义不确定性原理、修正统计及扩展引力理论产生的主要修正与推广。随后，我们讨论熵在宇宙学中被应用的三种概念上不同的方式。第一种是通过时空热力学猜想，其中引力动力学从应用于宇宙学视界的热力学关系中涌现，而广义熵形式因此导致修正的宇宙学演化。第二种是全息方法，其中熵界约束宇宙的真空能量，从而产生全息暗能量情景及其各种扩展。第三种是熵引力，其中引力被解释为熵起源的涌现现象，导致有趣的宇宙学现象学。通过回顾这些熵框架的理论基础与宇宙学含义，我们旨在阐明熵的作用，讨论开放问题，并勾勒出朝向对引力与宇宙学进行更深入热力学与信息理解的方向。
英文摘要
Entropy has emerged as a key concept at the intersection of gravity, quantum theory, and cosmology, revealing deep connections between geometry, information, and thermodynamics. The realization that black holes are thermodynamic systems, characterized by an entropy proportional to their horizon area, has provided evidence that spacetime itself may possess a microscopic structure. Since then, entropy has acquired a central role across quantum field theory, holography, quantum gravity, and cosmology. In this review, we present a unified account of entropy in gravitational and cosmological contexts. We first survey entropy in gravitational systems, focusing on black-hole thermodynamics, entropy bounds, the holographic principle, entanglement entropy, and the area law, together with the main corrections and generalizations arising from quantum field theory, generalized uncertainty principles, modified statistics, and extended theories of gravity. We then discuss three conceptually distinct ways in which entropy is employed in cosmology. The first is through the spacetime-thermodynamics conjecture, in which gravitational dynamics emerge from thermodynamic relations applied to cosmological horizons, and generalized entropy forms consequently lead to modified cosmological evolution. The second is the holographic approach, in which entropy bounds constrain the vacuum energy of the Universe, giving rise to the holographic dark energy scenario and its various extensions. The third is entropic gravity, where gravity is interpreted as an emergent phenomenon of entropic origin, leading to interesting cosmological phenomenology. By reviewing the theoretical foundations and cosmological implications of these entropic frameworks, we aim to clarify the role of entropy, discuss open issues and outline directions toward a deeper thermodynamic and informational understanding of gravity and cosmology.
Comments132 pages, 26 figures
