The aim of the seminar is to provide a direct new approach to Logarithmic Sobolev Inequalities LSI based on fundamental principles of Quantum Statistical Mechanics and involving properties of the Helmotz Free Energy and Relative Entropy of States.
After showing examples concerning Gross’ Gaussian LSI, Euclidean Sobolev Inequality and generator of Levy processes on compact (quantum) groups it will be shown an application to the infinite dimensional case of an Ideal Bose Gas in finite volume providing a lower bound on its pressure.