TY - JOUR

T1 - Correction to

T2 - Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems (Journal of Statistical Physics, (2020), 178, 2, (319-378), 10.1007/s10955-019-02434-w)

AU - Carlen, Eric A.

AU - Maas, Jan

N1 - Funding Information:
E.C. gratefully acknowledges support through NSF grant DMS-174625. J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117), and by the Austrian Science Fund (FWF), Project SFB F65.

PY - 2020/12

Y1 - 2020/12

N2 - The claimed bound Ric(A,∇, τ) ≥ γ in Theorem 10.6 in our paper [1] is unfortunately incorrect, as pointed out in [2]. A small modification of the proof shows that the weaker estimate Ric(A,∇, τ) ≥ γ 2 holds. This bound can be obtained by replacing (10.5) by the following computation, using the scalar inequalities (formula presented)On thematrix algebraMn(C), it is possible to improve the curvature bound γ/2 to γ/2 (1+ 1 n ), using the scalar inequality ∂1^(a, b) + ∂2^(a, b) ≥ 1 ≥ 1 n ^(a, b) for 0 < a, b ≤ n. We thank Michael Brannan and Li Gao and Marius Junge for pointing out the error, and Melchior Wirth and Haonan Zhang for useful discussions.

AB - The claimed bound Ric(A,∇, τ) ≥ γ in Theorem 10.6 in our paper [1] is unfortunately incorrect, as pointed out in [2]. A small modification of the proof shows that the weaker estimate Ric(A,∇, τ) ≥ γ 2 holds. This bound can be obtained by replacing (10.5) by the following computation, using the scalar inequalities (formula presented)On thematrix algebraMn(C), it is possible to improve the curvature bound γ/2 to γ/2 (1+ 1 n ), using the scalar inequality ∂1^(a, b) + ∂2^(a, b) ≥ 1 ≥ 1 n ^(a, b) for 0 < a, b ≤ n. We thank Michael Brannan and Li Gao and Marius Junge for pointing out the error, and Melchior Wirth and Haonan Zhang for useful discussions.

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U2 - 10.1007/s10955-020-02671-4

DO - 10.1007/s10955-020-02671-4

M3 - Comment/debate

AN - SCOPUS:85096129070

VL - 181

SP - 2432

EP - 2433

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 6

ER -