Thermodynamics of the most generalized form of holographic dark energy and some particular cases with corrected entropies

A four-parameter generalized entropy has recently been developed based on the generalized cut-off of holographic dark energy (HDE) formalism. It reduces to various known entropies for appropriate parameter limits, as shown in recent studies by Odintsov and others. In the current work, we investigate the evolution of the universe in its early and late phases within the framework of entropic cosmology, where the entropic energy density functions are reconstructed within the framework of the equivalence of holographic dark energy and four-parameter generalized entropy ($S_g$). Also, we examined different entropic dark energy models in this regard, including the generalized holographic dark energy with Nojiri-Odintsov(NO) cut-off, the Barrow entropic HDE (BHDE), and the Tsallis entropic HDE (THDE) as IR cut-off, all of three particular cases of the most generalized four parameter entropic holographic dark energy. Inspired by the works of Nojiri and others, our current work reports a study on cosmological parameters and thermodynamics with entropy corrections to cosmological horizon entropy as well as black hole entropy with a highly generalized viscous coupled holographic dark fluid along with its particular cases.