  Hard spherocylinders (cylinders of length $L$ and diameter $D$ capped at both
ends with two hemispheres) provide a suitable model for investigating
entropy-driven, mesophase formations in real colloidal fluids that are composed
of rigid rodlike molecules. We performed extensive Monte Carlo simulations of
this model fluid for elongations in the range $3 \leq L/D \leq 5$ and up to
$L/D = 20$, in order to investigate the relative importance of translational
and orientational correlations allowing for the emergence of nematic or smectic
order in the framework of the so-called residual multi-particle entropy (RMPE).
The vanishing of this quantity, which includes the re-summed contributions of
all spatial correlations involving more than two particles, signals the
structural changes which take place, at increasing densities, in the isotropic
fluid. We found that the ordering thresholds detected through the zero-RMPE
condition systematically correlate with the corresponding phase-transition
points, whatever the nature of the higher-density phase coexisting with the
isotropic fluid.
