  We study the thermodynamics of galaxy clusters in a modified Newtonian
potential motivated by a general solution to Newton's "sphere-point"
equivalence theorem. We obtain the $N$ particle partition function by
evaluating the configurational integral while accounting for the extended
nature of galaxies (via the inclusion of the softening parameter $\epsilon$
into the potential energy function). This softening parameter takes care of the
galaxy-halos whose effect on structuring the shape of the galactic disc has
been found recently. The spatial distribution of the particles (galaxies) is
also studied in this framework. A comparison of the new clustering parameter
$b_+$ to the original clustering parameters is presented in order to visualize
the effect of the modified gravity. We also discuss the possibility of system
symmetry breaking via the behavior of the specific heat as a function of
temperature.
