  Based on thermodynamics, we study the galactic clustering of an expanding
Universe by considering the logarithmic and volume (quantum) corrections to
Newton's law along with the repulsive effect of a harmonic force induced by the
cosmological constant ($\Lambda$) in the formation of the large scale structure
of the Universe. We derive the $N$-body partition function for extended-mass
galaxies (galaxies with halos) analytically. For this partition function, we
compute the exact equations of states, which exhibit the logarithmic, volume
and cosmological constant corrections. In this setting, a modified correlation
(clustering) parameter (due to these corrections) emerges naturally from the
exact equations of state. We compute a corrected grand canonical distribution
function for this system. Furthermore, we obtain a deviation in differential
forms of the two-point correlation functions for both the point-mass and
extended-mass cases. The consequences of these deviations on the correlation
function's power law are also discussed.
