  The effects of compressibility on Rayleigh-Taylor instability (RTI) are
investigated by inspecting the interplay between thermodynamic and hydrodynamic
non-equilibrium phenomena (TNE, HNE, respectively) via a discrete Boltzmann
model (DBM). Two effective approaches are presented, one tracking the evolution
of the \emph{local} TNE effects and the other focussing on the evolution of the
mean temperature of the fluid, to track the complex interfaces separating the
bubble and the spike regions of the flow. It is found that, both the
compressibility effects and the \emph{global} TNE intensity show opposite
trends in the initial and the later stages of the RTI. Compressibility delays
the initial stage of RTI and accelerates the later stage. Meanwhile, the TNE
characteristics are generally enhanced by the compressibility, especially in
the later stage. The global or mean thermodynamic non-equilibrium indicators
provide physical criteria to discriminate between the two stages of the RTI.
