Thermodynamics and phase transitions of galactic clustering in higher-order modified gravity

We study the thermodynamics of galactic clustering under the higher-order corrected Newtonian dynamics. The clustering of galaxies is considered as a gravitational phase transition. In order to study the effects of higher-order correction to the thermodynamics of gravitational system, we compute more exact equations of state. Moreover, we investigate the corrected probability distribution function for such a gravitating system. A relation between order parameter and the critical temperature is also established.