The current article is base on the concept of interacting dark matter in the framework of Extended Bose–Einstein condensate dark matter with the holographic dark energy model. In the scenario of dark energy and different cases of the dark matter interaction term, we discuss the behavior of the cosmological parameters, thermodynamics and thermal equilibrium conditions. To investigate the accelerated expansion or decelerated phase of the universe, we consider the observational values from literature of all parameters and graphically examine the different phases of the cosmological parameters which are deceleration, equation of state, jerk and snap parameters. We also graphically discuss the stability condition of the generalized second law of thermodynamics and thermal equilibrium condition by utilizing the observational values. We conclude that for all cases the deceleration parameter represents the accelerated behavior and for all cases the universe is stable for generalized second law of thermodynamics and for two cases the thermal equilibrium condition is stable and for third case it shows the partial stability.
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