On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems

@article{Bardet2019OnTM,
  title={On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems},
  author={Ivan Bardet and {\'A}ngela Capel and Angelo Lucia and David P'erez-Garc'ia and Cambyse Rouz'e},
  journal={arXiv: Quantum Physics},
  year={2019}
}
The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure, via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic… 

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