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Conventional equilibrium statistical mechanics of open gravitational systems is known to be problematical. We first recall that spherical stars/galaxies acquire unbounded radii, become infinitely massive, and evaporate away continuously if one uses the standard Maxwellian distribution fB  (which maximizes the usual Boltzmann-Shannon entropy and hence has a tail extending to infinity). Next, we show that these troubles disappear automatically if we employ the exact most probable distribution  f  (which maximizes the combinatorial entropy and hence possesses a sharp cutoff tail). Finally, if astronomical observation is carried out on a large galaxy, then the Poisson equation together with thermal de Broglie wavelength provides useful information about the cutoff radius rK, cutoff energy  εK, and the huge quantum number K up to which the cluster exists. Thereby, a refinement over the empirical lowered isothermal King models, is achieved. Numerically, we find that the most probable distribution (MPD) prediction fits well the number density profile near the outer edge of globular clusters

Entropy Maximization, Cutoff Distribution, and Finite Stellar Masses