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This article proposes a modification in the Sharma-Mittal entropy anddistinguishes it as generalised Tsallis entropy. This modification accomplishthe Sharma-Mittal entropy to be used in classical information theory. We derivea product rule $$(xy)^{r + k} \ln_{\{k,r\}}(xy) = x^{r + k} \ln_{\{k,r\}}(x) +y^{r + k} \ln_{\{k,r\}}(y) + 2k x^{r + k} y^{r + k}\ln_{\{k,r\}}(x)\ln_{\{k,r\}}(y),$$ for the two-parameter deformed logarithm$\ln_{\{k,r\}}(x) = x^r \frac{x^k - x^{-k}}{2k}$. It assists us to derive anumber of information theoretic properties of the generalized Tsallis entropy,and related entropy. They include the sub-additive property, strongsub-additive property, joint convexity, and information monotonicity. Thisarticle is an exposit investigation on the information-theoretic, andinformation-geometric characteristics of generalized Tsallis entropy.

Elements of Generalized Tsallis Relative Entropy in Classical Information Theory