  The core collapse of massive, rapidly-rotating stars are thought to be the
progenitors of long-duration gamma-ray bursts (GRB) and their associated
hyper-energetic supernovae (SNe). At early times after the collapse, relatively
low angular momentum material from the infalling stellar envelope will
circularize into an accretion disk located just outside the black hole horizon,
resulting in high accretion rates necessary to power a GRB jet. Temperatures in
the disk midplane at these small radii are sufficiently high to dissociate
nuclei, while outflows from the disk can be neutron-rich and may synthesize
r-process nuclei. However, at later times, and for high progenitor angular
momentum, the outer layers of the stellar envelope can circularize at larger
radii $\gtrsim 10^{7}$ cm, where nuclear reaction can take place in the disk
midplane ((e.g.~$^{4}$He + $^{16}$O $\rightarrow$ $^{20}$Ne + $\gamma$).. Here
we explore the effects of nuclear burning on collapsar accretion disks and
their outflows by means of hydrodynamical $\alpha$-viscosity torus simulations
coupled to a 19-isotope nuclear reaction network, which are designed to mimic
the late infall epochs in collapsar evolution when the viscous time of the
torus has become comparable to the envelope fall-back time. Our results address
several key questions, such as the conditions for quiescent burning and
accretion versus detonation and the generation of $^{56}$Ni in disk outflows,
which we show could contribute significantly to powering GRB supernovae. Being
located in the slowest, innermost layers of the ejecta, the latter could
provide the radioactive heating source necessary to make the spectral
signatures of r-process elements visible in late-time GRB-SNe spectra.
