Entropic approach to Brownian movement

A diffusional driving force, called the radial force, which is responsible for the increase with time of the scalar separation between a fixed point and a particle undergoing three‐dimensional Brownian motion, is derived using Boltzmann’s equation. The radial force is used to derive several results from the classical theory of Brownian motion, namely Einstein’s 〈x2〉 = 2Dt equation and the expression for the one‐dimensional harmonic oscillator. The radial force concept is then extended to establish a thermodynamic criterion for the occurrence of a melting transition in a liquid whose particles attract one another by means of centrally symmetric forces. The theory, when applied to the alkali halide and alkaline‐earth oxide molten salts, accurately predicts the observed melting temperatures. The definition of the dielectric constant used in the ionic salt fusion theory also provides a basis for understanding molten salt surface tensions. Finally, the radial force is used to demonstrate that an ideal rubber n...