  We study the properties of cosmological density perturbations in a
multi-component system consisting of a scalar field and a perfect fluid. We
discuss the number of degrees of freedom completely describing the system,
introduce a full set of dynamical gauge-invariant equations in terms of the
curvature and entropy perturbations, and display an efficient formulation of
these equations as a first-order system linked by a fairly sparse matrix. Our
formalism includes spatial gradients, extending previous formulations
restricted to the large-scale limit, and fully accounts for the evolution of an
isocurvature mode intrinsic to the scalar field. We then address the issue of
the adiabatic condition, in particular demonstrating its preservation on large
scales. Finally, we apply our formalism to the quintessence scenario and
clearly underline the importance of initial conditions when considering
late-time perturbations. In particular, we show that entropy perturbations can
still be present when the quintessence field energy density becomes
non-negligible.
