Thermodynamics and galactic clustering with a modified gravitational
  potential
  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.
