  We propose an additional category of dimensionless groups based on the
principle of {\it entropic similarity}, defined by ratios of (i) entropy
production terms; (ii) entropy flow rates or fluxes; or (iii) information flow
rates or fluxes. Since all processes involving work against friction,
dissipation, diffusion, dispersion, mixing, separation, chemical reaction, gain
of information or other irreversible changes are driven by (or must overcome)
the second law of thermodynamics, it is appropriate to analyse these processes
directly in terms of competing entropy-producing and transporting phenomena and
the dominant entropic regime, rather than indirectly in terms of forces. In
this study, we derive entropic groups for a wide variety of phenomena relevant
to fluid mechanics, classified into diffusion and chemical reaction processes,
dispersion mechanisms and wave phenomena. It is shown that many dimensionless
groups traditionally derived by kinematic or dynamic similarity (including the
Reynolds number) can also be recovered by entropic similarity -- albeit with a
different entropic interpretation -- while a large number of new dimensionless
groups are also identified. The analyses significantly expand the scope of
dimensional analysis and similarity arguments for the resolution of new and
existing problems in science and engineering.
