  Traditional random-walk particle-tracking (PT) models of advection and
dispersion do not track entropy, because particle masses remain constant. Newer
mass-transfer particle tracking (MTPT) models have the ability to do so because
masses of all compounds may change along trajectories. Additionally, the
probability mass functions (PMF) of these MTPT models may be compared to
continuous solutions with probability density functions, when a consistent
definition of entropy (or similarly, the dilution index) is constructed. This
definition reveals that every numerical model incurs a computational entropy.
Similar to Akaike's entropic penalty for larger numbers of adjustable
parameters, the computational complexity of a model (e.g., number of nodes)
adds to the entropy and, as such, must be penalized. The MTPT method can use a
particle-collision based kernel or an SPH-derived adaptive kernel. The latter
is more representative of a locally well-mixed system (i.e., one in which the
dispersion tensor equally represents mixing and solute spreading), while the
former better represents the separate processes of mixing versus spreading. We
use computational means to demonstrate the viability of each of these methods.
