Generalised (Non-singular) Entropy Functions with Applications to Cosmology and Black Holes

The growing interest of different entropy functions proposed so far (like the Bekenstein-Hawkinh, Tsallis, Rényi, 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.