@article{6358,
  abstract     = {We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras.  Our settingcovers  arbitrary  skew-derivations  and  it  provides  a  unified  framework  that  simultaneously  generalizes  recently  constructed  transport  metrics  for  Markov  chains,  Lindblad  equations,  and  the  Fermi  Ornstein–Uhlenbeck  semigroup.   We  develop  a  non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature  bounds,  logarithmic  Sobolev  inequalities,  transport-entropy  inequalities,  andspectral gap estimates.},
  author       = {Carlen, Eric A. and Maas, Jan},
  issn         = {1572-9613},
  journal      = {Journal of Statistical Physics},
  number       = {2},
  pages        = {319--378},
  publisher    = {Springer Nature},
  title        = {{Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems}},
  doi          = {10.1007/s10955-019-02434-w},
  volume       = {178},
  year         = {2020},
}