A modified Bakry-\'Emery 2 criterion inequality and the monotonicity of the Tsallis entropy
Abstract
The Bakry-\'Emery 2 criterion inequality provides a method for establishing the logarithmic Sobolev inequality. We prove a one-parameter family of weighted Bakry-\'Emery 2 criterion inequalities which in the limit case yields the improved constant due to Ji Ji24. Furthermore, we establish a modified weighted 2 criterion inequality which could be interpreted as a monotonicity of the Tsallis entropy under the heat flow and yields a family of sharp Sobolev inequalities.
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