arXiv subjects

Jincheng Wan

Publications and source records attributed to Jincheng Wan.

2 recordsLinked to original sources

arXiv2026

Some entropic inequalities for primitive KMS symmetric quantum Markov semigroups

In this note, we prove that every primitive KMS-symmetric quantum Markov semigroup on a finite-dimensional matrix algebra satisfies a modified logarithmic Sobolev inequality (MLSI). We also construct a primitive quantum Markov semigroup without KMS symmetry that fails MLSI, and a primitive KMS-symmetric quantum Markov semigroup that fails complete MLSI (CMLSI). The latter construction also provides a non-primitive KMS-symmetric quantum Markov semigroup without MLSI. For the graph-based KMS-symmetric quantum Markov semigroups studied here, we prove MLSI and CMLSI when the underlying graph is connected and has at least three vertices. Finally, we establish CMLSI for a class of primitive bimodule KMS-symmetric quantum Markov semigroups arising from fermionic systems.

math.OA↗

arXiv2026

Bimodule KMS Symmetric Quantum Markov Semigroups and Gradient Flows

The bimodule KMS symmetry of a bimodule quantum Markov semigroup extends the classical KMS symmetry of a quantum Markov semigroup. Compared with (bimodule) GNS symmetry, the (bimodule) KMS symmetry retains significantly more of the underlying noncommutativity. In this paper, we study bimodule KMS symmetric quantum Markov semigroups and introduce directional matrices for such semigroups, which reduce to diagonal matrices in the GNS symmetric setting. Using these directional matrices, we establish a corresponding gradient-flow structure. As a consequence, we obtain both a modified logarithmic Sobolev inequality and a Talagrand inequality for bimodule KMS symmetric quantum Markov semigroups.

math.OA↗