  This paper concludes a three-Part series on the limits the laws of physics
place on the sustained performance of reversible computers. Part I concerned
aggregate performance in terms of computational operations per unit time, but
neglected to consider interactions among computational sub-units or between
computational sub-units and shared resources such as memory or chemical
species. Part II extended the analysis to consider the former set of
interactions. In this Part we extend the analysis to consider the latter set,
with a particular focus on resource distribution in the first half. It is found
that most schemes imaginable fail to function effectively in the limit of
vanishing 'computational bias' $b$, which measures the net fraction of
transitions which are successful, and falls as the system grows in size.
Driving thermodynamically unfavourable reactions, such as resource
distribution, is a very general problem for such systems and can be solved by
supplying a sufficient excess of free energy. We propose a scheme to
dynamically supply enough free energy for a given reaction, automatically and
rapidly adapting to changes in the disequilibrium state of said
reaction--including the case when the favourable reaction direction switches.
The overhead of this scheme is no worse than the overhead found in Part II for
communicating reversible computers under the same regime.
