标题： 广义（非奇异）熵函数及其在宇宙学和黑洞中的应用 显示英文标题

标题： Generalised (non-singular) entropy functions with applications to cosmology and black holes

摘要： 到目前为止，不同熵函数（如贝肯斯坦-霍金熵、Tsallis熵、Rényi熵、巴罗熵、Sharma-Mittal熵、Kaniadakis熵和圈量子引力熵）在黑洞热力学以及宇宙学中的日益增长的兴趣，自然引发了这样一个问题：是否存在一个广义的熵函数，能够概括所有这些已知的熵。 本着这种精神，我们提出了一种新的四参数熵函数，似乎在熵参数的某些极限情况下会收敛到上述已知的熵。 广义熵的提出扩展到了非奇异情况，在这种情况下，熵在整个宇宙的宇宙学演化过程中都是无奇点的。 这种广义熵的特征是，它有助于我们从根本上理解一个重要物理量“熵”。 因此，我们讨论了广义熵对黑洞热力学以及宇宙学的影响，并从不同角度讨论了熵参数的各种约束。 显示英文摘要

摘要： The growing interest of different entropy functions proposed so far (like the Bekenstein-Hawking, Tsallis, R\'{e}nyi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies) towards black hole thermodynamics as well as towards cosmology lead to the natural question that whether there exists a generalized entropy function that can generalize all these known entropies. With this spirit, we propose a new 4-parameter entropy function that seems to converge to the aforementioned known entropies for certain limits of the entropic parameters. The proposal of generalized entropy is extended to non-singular case, in which case, the entropy proves to be singular-free during the entire cosmological evolution of the universe. The hallmark of such generalized entropies is that it helps us to fundamentally understand one of the important physical quantities namely ``entropy''. Consequently we address the implications of the generalized entropies on black hole thermodynamics as well as on cosmology, and discuss various constraints of the entropic parameters from different perspectives.