D. N. Tripathi

Entropy Maximization, Cutoff Distribution, and Finite Stellar Masses

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 (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 (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 , cutoff energy , and the huge quantum number 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.

New insights into optical Fourier transforms, radial distribution function, and Glatter’s method

We address several subtle issues concerning the static scattering of light or x-rays from physical/chemical/biological systems. In the context of Fourier integrals we point out that the Glatter–Moore algorithms can efficiently perform sine inversion between two functions J(q) and L(r) of calculus, and the structure factor S(q) can be correct only if the asymptotic value of the pair correlation function differs from unity. Next, concerning the radial distribution function g(r), we derive a new integral equation for and use it to find the effective potential when the input pair potential is parabolic. Finally, turning to data analysis, we demonstrate that a bump in the underlying distance distribution function P(r) plays a major role in producing attenuated oscillations in the experimental structure factor, and also in the study of a subtle convolution integral.