---
res:
bibo_abstract:
- We study a class of ergodic quantum Markov semigroups on finite-dimensional unital
C⁎-algebras. These semigroups have a unique stationary state σ, and we are concerned
with those that satisfy a quantum detailed balance condition with respect to σ.
We show that the evolution on the set of states that is given by such a quantum
Markov semigroup is gradient flow for the relative entropy with respect to σ in
a particular Riemannian metric on the set of states. This metric is a non-commutative
analog of the 2-Wasserstein metric, and in several interesting cases we are able
to show, in analogy with work of Otto on gradient flows with respect to the classical
2-Wasserstein metric, that the relative entropy is strictly and uniformly convex
with respect to the Riemannian metric introduced here. As a consequence, we obtain
a number of new inequalities for the decay of relative entropy for ergodic quantum
Markov semigroups with detailed balance.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Eric
foaf_name: Carlen, Eric
foaf_surname: Carlen
- foaf_Person:
foaf_givenName: Jan
foaf_name: Maas, Jan
foaf_surname: Maas
foaf_workInfoHomepage: http://www.librecat.org/personId=4C5696CE-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-0845-1338
bibo_doi: 10.1016/j.jfa.2017.05.003
bibo_issue: '5'
bibo_volume: 273
dct_date: 2017^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/00221236
dct_language: eng
dct_publisher: Academic Press@
dct_title: Gradient flow and entropy inequalities for quantum Markov semigroups
with detailed balance@
...