Abstract Focusing on the description of cosmic evolution at late times, this study examines a generalized holographic dark energy (HDE) framework constructed via a polynomial expansion in the Hubble parameter, which includes contributions proportional to H^2, H 2, H^4, H 4, and H^6, H 6, introduced through a variable parameter within the standard holographic formula. The analysis is carried out in the context of a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe, consisting of non-interacting matter together with the HDE fluid. We obtain the full set of Friedmann equations to investigate cosmic evolution and then analyze the system to determine whether thermodynamic P-v P - v type phase transitions can occur.
Cruz et al. (Mon,) studied this question.