  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 gravitating system. A relation between order
parameter and the critical temperature is also established.
