 Log sum inequality

For nonnegative $a_i,b_i$, with $a={\sum }_i{a}_i$ and $b={\sum }_i{b}_i$, the log-sum inequality isIt proves both Gibbs inequality and the data processing inequality for relative entropy.

The log-sum inequality, also known as Jensen's inequality in the context of convex functions, relates to the properties of logarithmic functions and the concavity of such functions.