Rayleigh-Taylor (RT) instability widely exists in nature and engineering fields.How to better under-stand 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 meth-ods.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 insta-bility.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.