Semigroups of completely positive trace preserving maps satisfying a certain detailed balance condition are gradient flow driven by dissipation of the quantum relative entropy with respect to a non-commutative analog of the 2-Wasserstein metric on the space of probability densities on Euclidean space. As in the classical case, this way of viewing the evolution equations solved by these semigroups leads to sharp entropy production inequalities. This perspective has resolved some recent conjectures in quantum information theory. This is joint work with Jan Maas.

# Mathematical Physics Seminar

Organizer(s):

For more information about this seminar, contact Michael Aizenman

**Please click on seminar title for complete abstract.**

October 24, 2017

4:30pm - 5:30pm

##### Quantum Markov Semigroups with detailed balance as gradient flow for relative entropy and entropy production inequalities

Location

Jadwin Hall 343

Speaker: Eric Carlen,

Rutgers University

Rutgers University

November 7, 2017

4:30pm - 5:30pm

##### Hydrodynamics of integrable classical and quantum systems

Discussed is the Euler-type hydrodynamics for one-dimensional integrable quantum systems, as the Lieb-Liniger delta Bose gas and the XXZ chain. Of particular interest are domain wall initial states. We will use classical hard rods as an illustration of the underlying structure.

Location

Jadwin Hall 343

Speaker: Herbert Spohn ,

Technical University Munich and Columbia University

Technical University Munich and Columbia University

November 28, 2017

4:30pm - 5:30pm

##### TBA - Dr. Efi Efrati

Location

Jadwin Hall 343

Speaker: Dr. Efi Efrati,

Weizmann Institute

Weizmann Institute