  We investigate the Cauchy problem to the compressible planar non-resistive
magnetohydrodynamic equations with zero heat conduction. The global existence
of strong solutions to such a model has been established by Li and Li (J.
Differential Equations 316: 136--157, 2022). However, to our best knowledge, so
far there is no result on the behavior of the entropy near the vacuum region
for this model. The main novelty of this paper is to give a positive response
to this problem. More precisely, by a series of a priori estimates, especially
the singular type estimates, we show that the boundedness of the entropy can be
propagated up to any finite time provided that the initial vacuum presents only
at far fields with sufficiently slow decay of the initial density.
