Gradient flows and entropy inequalities in dissipative quantum systems

Seminar | June 27 | 11 a.m.-12 p.m. | 1011 Evans Hall

 Jan Maas, IST Austria

 Department of Statistics

At the end of the 1990s it was discovered by
Jordan/Kinderlehrer/Otto that the diffusion equation is a gradient flow
in the space of probability measures, where the driving functional is
the Boltzmann-Shannon entropy, and the dissipation mechanism is given by
the 2-Wasserstein metric from optimal transport. This result has been
the starting point for striking developments at the interface of
analysis, probability, and metric geometry.
In this talk I will review recent work, in which we introduced new
optimal transport metrics that yield gradient flow descriptions for
dissipative quantum systems satisfying detailed balance. This allows us
to obtain sharp rates of convergence to equilibrium in several examples.
The talk is based on joint work with Eric Carlen.