A modified Bakry-Émery $\hat{I}{“}_2$ criterion inequality and the monotonicity of the Tsallis entropy

Xiaohan Cai, Xiaodong Wang

The Bakry-Émery $\hat{I}{“}_2$ criterion inequality provides a method for establishing the logarithmic Sobolev inequality. We prove a one-parameter family of weighted Bakry-Émery $\hat{I}{“}_2$…