  We introduce a simple entropy-based formalism to characterize the role of
mixing in pressure-balanced multiphase clouds, and demonstrate example
applications using Enzo-E (magneto)hydrodynamic simulations. Under this
formalism, the high-dimensional description of the system's state at a given
time is simplified to the joint distribution of mass over pressure ($P$) and
entropy ($K=P/\rho^\gamma$). As a result, this approach provides a way for
(empirically and analytically) quantifying the impact of different initial
conditions and sets of physics on the system evolution. We find that mixing
predominantly alters the distribution along the $K$ direction and illustrate
how the formalism can be used to model mixing and cooling for fluid elements
originating in the cloud. We further confirm and generalize a previously
suggested criterion for cloud growth in the presence of radiative cooling, and
demonstrate that the shape of the cooling curve, particularly at the low
temperature end, can play an important role in controlling condensation.
Moreover, we discuss the capacity of our approach to generalize such a
criterion to apply to additional sets of physics, and to build intuition for
the impact of subtle higher order effects not directly addressed by the
criterion.
