A note on the equivalence of a barotropic perfect fluid with a K-essence
  scalar field
  In this short note, we obtain the necessary and sufficient condition for a
class of non-canonical single scalar field models to be exactly equivalent to
barotropic perfect fluids, under the assumption of an irrotational fluid flow.
An immediate consequence of this result is that the non-adiabatic pressure
perturbation in this class of scalar field systems vanishes exactly at all
orders in perturbation theory and on all scales. The Lagrangian for this
general class of scalar field models depends on both the kinetic term and the
value of the field. However, after a field redefinition, it can be effectively
cast in the form of a purely kinetic K-essence model.
