  Rayleigh-Taylor (RT) instability widely exists in nature and engineering
fields. How to better understand the physical mechanism of RT instability is of
great theoretical significance and practical value. At present, abundant
results of RT instability have been obtained by traditional macroscopic
methods. However, research on the thermodynamic non-equilibrium (TNE) effects
in the process of system evolution is relatively scarce. In this paper, the
discrete Boltzmann method based on non-equilibrium statistical physics is
utilized to study the effects of the specific heat ratio on compressible RT
instability. The evolution process of the compressible RT system with different
specific heat ratios can be analyzed by the temperature gradient and the
proportion of the non-equilibrium region. Firstly, as a result of the
competition between the macroscopic magnitude gradient and the non-equilibrium
region, the average TNE intensity first increases and then reduces, and it
increases with the specific heat ratio decreasing; the specific heat ratio has
the same effect on the global strength of the viscous stress tensor. Secondly,
the moment when the total temperature gradient in y direction deviates from the
fixed value can be regarded as a physical criterion for judging the formation
of the vortex structure. Thirdly, under the competition between the temperature
gradients and the contact area of the two fluids, the average intensity of the
non-equilibrium quantity related to the heat flux shows diversity, and the
influence of the specific heat ratio is also quite remarkable.
