  The use of charge balance functions in heavy-ion collision studies was
initially proposed as a probe of delayed hadronization and two-stage quark
production in these collisions. It later emerged that general balance functions
can also serve as a probe of the diffusivity of light quarks as well as the
evolution of the systems formed in heavy-ion collisions. In this work, we
reexamine the formulation of general balance functions and consider how to best
define and measure these correlation functions in terms of differences of
conditional densities of unlike-sign and like-sign particle pairs. We define
general balance functions in terms of associated particle functions and show
these obey a simple sum rule. We additionally proceed to distinguish between
balance functions expressed as differences of conditional densities valid
irrespective of experimental acceptance boundaries and bound balance functions
that explicitly account for the limited acceptance of experiments. General
balance functions are additionally extended to accommodate strange, baryon, as
well as charm and bottom quantum numbers based on the densities of these
quantum numbers.
