  A complex balanced kinetic system is absolutely complex balanced (ACB) if
every positive equilibrium is complex balanced. Two results on absolute complex
balancing were foundational for modern chemical reaction network theory (CRNT):
in 1972, M. Feinberg proved that any deficiency zero complex balanced system is
absolutely complex balanced. In the same year, F. Horn and R. Jackson showed
that the (full) converse of the result is not true: any complex balanced mass
action system, regardless of its deficiency, is absolutely complex balanced. In
this paper, we revive the study of ACB systems first by providing a partial
converse to Feinberg's Theorem. In the spirit of Horn and Jackson's result, we
then describe several methods for constructing new classes of ACB systems with
positive deficiency and present classes of power law kinetic systems for each
method. Furthermore, we illustrate the usefulness of the ACB property for
obtaining new results on absolute concentration robustness (ACR) in a species,
a concept introduced for mass action systems by Shinar and Feinberg in 2010,
for a class of power law systems. Finally, we motivate the study of ACB in
poly-PL systems, i.e. sums of power law systems, and indicate initial results.
