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We propose a new entropy construct that generalizes the Tsallis, R\'enyi,Sharma-Mittal, Barrow, Kaniadakis, and Loop Quantum Gravity entropies andreduces to the Bekenstein-Hawking entropy in a certain limit. This proposal isapplied to the Schwarzschild black hole and to spatially homogeneous andisotropic cosmology, where it is shown that it can potentially describeinflation and/or holographic dark energy.

How fundamental is entropy? From non-extensive statistics and black hole physics to the holographic dark universe