Extended uncertainty principle and equation of state for dark energy

The modification of Heisenberg's uncertainty principle (HUP), is considered valuable in modern theoretical physics due to its implications on quantum gravity effects. In this paper, we attempted to derive an equation of state for dark energy, using the extended uncertainty principle (EUP) which includes a defined maximum length. We then compared this novel equation with the equations of state obtained from cosmological observations. The observational constraints on dark energy equation of states and the second law of thermodynamics suggest that the EUP parameter sign with maximum length must change.