Thermodynamic origin of the Cardassian universe

In the Cadassian universe, one can explain the acceleration of the universe without introducing a dark energy component. However, it is hard to get the dynamical equations of this model from the action principle. Recently, works on the relation between thermodynamics and gravity indicate that gravity force may not be a fundamental force. In this paper, we shall study the thermodynamics of the Cardassian universe, and it might be the origin of this cosmological model. We find that the corresponding entropy obeys ordinary area law when the area of the trapping horizon is small, and it becomes a constant when the area is going to be large in the original and modified polytropic Cardassian models, while it has a maximum value in the exponential one. It seems that the Cardassian universe only contains finite information according to the holographic principle, which states that all the information in the bulk should be encoded on the boundary of the bulk.