  The antiproton-to-proton ratio in the cosmic-ray spectrum is a sensitive
probe of new physics. Using recent measurements of the cosmic-ray antiproton
and proton fluxes in the energy range of 1-1000 GeV, we study the contribution
to the $\bar{p}/p$ ratio from secondary antiprotons that are produced and
subsequently accelerated within individual supernova remnants. We consider
several well-motivated models for cosmic-ray propagation in the interstellar
medium and marginalize our results over the uncertainties related to the
antiproton production cross section and the time-, charge-, and
energy-dependent effects of solar modulation. We find that the increase in the
$\bar{p}/p$ ratio observed at rigidities above $\sim$ 100 GV cannot be
accounted for within the context of conventional cosmic-ray propagation models,
but is consistent with scenarios in which cosmic-ray antiprotons are produced
and subsequently accelerated by shocks within a given supernova remnant. In
light of this, the acceleration of secondary cosmic rays in supernova remnants
is predicted to substantially contribute to the cosmic-ray positron spectrum,
accounting for a significant fraction of the observed positron excess.
