  The classical theory of cluster relaxation is unsatisfactory because it
involves the Coulomb logarithm. The Balescu-Lenard (BL) equation provides a
rigorous alternative that has no ill-defined parameter. Moreover, the BL
equation, unlike classical theory, includes the cluster's self-gravity. A
heuristic argument is given that indicates that relaxation does not occur
predominantly through two-particle scattering and is enhanced by self-gravity.
The BL equation is adapted to a spherical system and used to estimate the flux
through the action space of isochrone clusters with different velocity
anisotropies. A range of fairly different secular behaviours is found depending
on the fraction of radial orbits. Classical theory is also used to compute the
corresponding classical fluxes. The BL and classical fluxes are very different
because (a) the classical theory materially under-estimates the impact of
large-scale collectively amplified fluctuations and (b) only the leading terms
in an infinite sum for the BL flux are computed. A complete theory of cluster
relaxation likely requires that the sum in the BL equation be decomposed into a
sum over a finite number of small wavenumbers complemented by an integral over
large wavenumbers analogous to classical theory.

Astrophysics of Galaxies