article published yes Melchior Wirth author 88644358-0A0E-11EA-8FA5-49A33DDC885E0000-0002-0519-4241 Haonan Zhang author D8F41E38-9E66-11E9-A9E2-65C2E5697425 JaMa department ISTplus - Postdoctoral Fellowships project Curvature-dimension in noncommutative analysis project Optimal Transport and Stochastic Dynamics project Taming Complexity in Partial Differential Systems project Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups. https://research-explorer.ista.ac.at/download/12087/14051/2023_AnnalesHenriPoincare_Wirth.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Springer Nature2023 eng 1424-0637 2105.08303 36950223 00083749980000210.1007/s00023-022-01220-x 24717-750 Wirth, M., &#38; Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. Springer Nature. <a href="https://doi.org/10.1007/s00023-022-01220-x">https://doi.org/10.1007/s00023-022-01220-x</a> M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 717–750, 2023. Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750. Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 717–50, doi:<a href="https://doi.org/10.1007/s00023-022-01220-x">10.1007/s00023-022-01220-x</a>. Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00023-022-01220-x">https://doi.org/10.1007/s00023-022-01220-x</a>. M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750. Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. 2023;24:717-750. doi:<a href="https://doi.org/10.1007/s00023-022-01220-x">10.1007/s00023-022-01220-x</a> 120872022-09-11T22:01:57Z2025-04-23T08:53:05Z