| Abstract: |
| The logarithmic Sobolev inequality is a functional inequality that means control of the Boltzmann--Shannon entropy by the Fisher information of probability density functions. It is well-known that the optimizer for this inequality is the Gauss function. In this talk, we consider the logarithmic Sobolev inequality for the Tsallis entropy, a one-parameter extension of the Boltzmann--Shannon entropy. We obtain deficit estimates for the logarithmic Sobolev inequality corresponding to the Tsallis entropy and consider its application to the generalized Heisenberg uncertainty relation. |
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