  Early studies on Rayleigh-Taylor instability (RTI) primarily relied on the
Navier-Stokes (NS) model. As research progresses, it becomes increasingly
evident that the kinetic information that the NS model failed to capture is of
great value for identifying and even controlling the RTI process;
simultaneously, the lack of analysis techniques for complex physical fields
results in a significant waste of data information. In addition, early RTI
studies mainly focused on the incompressible case and the weakly compressible
case. In the case of strong compressibility, the density of the fluid from the
upper layer (originally heavy fluid) may become smaller than that of the
surrounding (originally light) fluid, thus invalidating the early method of
distinguishing light and heavy fluids based on density. In this paper, tracer
particles are incorporated into a single-fluid discrete Boltzmann method (DBM)
model that considers the van der Waals potential. By using tracer particles to
label the matter-particle sources, a careful study of the matter-mixing and
energy-mixing processes of the RTI evolution is realized in the single-fluid
framework. The effects of compressibility on the evolution of RTI are examined
mainly through the analysis of bubble and spike velocities, the ratio of area
occupied by heavy fluid, and various entropy generation rates of the system. It
is demonstrated that: (1) compressibility has a suppressive effect on the spike
velocity, and this suppressive impact diminishes as the Atwood number ($At$)
increases. The influence of compressibility on bubble velocity shows a staged
behavior with increasing $At$. (2) The impact of compressibility on the entropy
production rate associated with the heat flow (${{\dot{S}}_{NOEF}}$) is related
to the stages of RTI evolution.
