article published yes Eric A. Carlen author Jan Maas author 4C5696CE-F248-11E8-B48F-1D18A9856A870000-0002-0845-1338 JaMa department IST Austria Open Access Fund project Optimal Transport and Stochastic Dynamics project Taming Complexity in Partial Differential Systems project 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. https://research-explorer.ista.ac.at/download/6358/7209/2019_JourStatistPhysics_Carlen.pdf application/pdfno Springer Nature2020 eng 0022-4715 1572-9613 1811.04572 33223567 00049893330000110.1007/s10955-019-02434-w 1782319-378 https://doi.org/10.1007/s10955-020-02671-4 Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” <i>Journal of Statistical Physics</i>, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:<a href="https://doi.org/10.1007/s10955-019-02434-w">10.1007/s10955-019-02434-w</a>. Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378. Carlen, E. A., &#38; Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. <i>Journal of Statistical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s10955-019-02434-w">https://doi.org/10.1007/s10955-019-02434-w</a> E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378. E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems,” <i>Journal of Statistical Physics</i>, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020. Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. <i>Journal of Statistical Physics</i>. 2020;178(2):319-378. doi:<a href="https://doi.org/10.1007/s10955-019-02434-w">10.1007/s10955-019-02434-w</a> Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href="https://doi.org/10.1007/s10955-019-02434-w">https://doi.org/10.1007/s10955-019-02434-w</a>. 63582019-04-30T07:34:18Z2025-06-12T07:27:20Z