Correction to: 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)

Eric A. Carlen, Jan Maas

Research output: Contribution to journalComment/debatepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2432-2433
Number of pages2
JournalJournal of Statistical Physics
Volume181
Issue number6
DOIs
StatePublished - Dec 2020

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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