# Mathematics Colloquia and Seminars

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### A Unified Treatment of Convexity of Relative Entropy and Related Trace Functions

**Mathematical Physics & Probability**

Speaker: | Marybeth Ruskai, Tufts University |

Location: | 3106 MSB |

Start time: | Tue, Nov 3 2009, 4:10PM |

A a simple, self-contained proof of joint convexity for a will be given for a generalization of relative entropy derived from the Wigner-Yanase- Dyson entropy. The monotonicity of relative entropy and strong subadditivity of quantum entropy then follow as easy corollaries. Moreover, this approach also gives conditions for equality and shows that they are the same for the entire class of functions considered. Equality conditions are also obtained for some matrix inequalities proved by Lieb and Carlen.