  Entropy stable schemes replicate an entropy inequality at the semi-discrete
level. These schemes rely on an algebraic summation-by-parts (SBP) structure
and a technique referred to as flux differencing. We provide simple and
efficient formulas for Jacobian matrices for the semi-discrete systems of ODEs
produced by entropy stable discretizations. These formulas are derived based on
the structure of flux differencing and derivatives of flux functions, which can
be computed using automatic differentiation (AD). Numerical results demonstrate
the efficiency and utility of these Jacobian formulas, which are then used in
the context of two-derivative explicit time-stepping schemes and implicit
time-stepping.
