  The paper describes the construction of entropy-stable discontinuous Galerkin
difference (DGD) discretizations for hyperbolic conservation laws on
unstructured grids. The construction takes advantage of existing theory for
entropy-stable summation-by-parts (SBP) discretizations. In particular, the
paper shows how DGD discretizations -- both linear and nonlinear -- can be
constructed by defining the SBP trial and test functions in terms of
interpolated DGD degrees of freedom. In the case of entropy-stable
discretizations, the entropy variables rather than the conservative variables
must be interpolated to the SBP nodes. A fully-discrete entropy-stable scheme
is obtained by adopting the relaxation Runge-Kutta version of the midpoint
method. In addition, DGD matrix operators for the first derivative are shown to
be dense-norm SBP operators. Numerical results are presented to verify the
accuracy and entropy-stability of the DGD discretization in the context of the
Euler equations. The results suggest that DGD and SBP solution errors are
similar for the same number of degrees of freedom. Finally, an investigation of
the DGD spectra shows that spectral radius is relatively insensitive to
discretization order; however, the high-order methods do suffer from the linear
instability reported for other entropy-stable discretizations.
