发表机构
School of Mathematics & Physics, Yancheng Institute of Technology; School of Physics, Hubei University（盐城工学院数学与物理学院; 湖北大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广Auconi经典非平衡弛豫不等式至量子马尔可夫动力学，利用BKM内积分解生成元，推导非平衡曲率修正的精确形式及其信息几何界，并在量子比特、qutrit及二维Fokker-Planck模型中验证。
AI 中文摘要
本文研究了量子马尔可夫动力学中短时非平衡弛豫背后的量子信息几何结构，并推导了短时弛豫曲率的非平衡修正的界。这些界将Auconi经典非平衡弛豫不等式背后的信息几何结构推广到量子马尔可夫动力学。我们采用von Neumann相对熵作为量子散度，并通过Kubo-Mori映射参数化扰动，该映射在任意温度下将相对熵的二阶展开转化为Bogoliubov-Kubo-Mori（BKM）内积。对于具有满秩稳态的量子马尔可夫半群，诱导的切空间生成元可规范分解为BKM对称部分和BKM反对称部分，且主导的非平衡曲率修正精确等于生成元的耗散部分与输运部分之间对易子的期望值。该修正受BKM对称耗散活动度与输运部门活动度之积的约束。该界在非对易量子比特模型和驱动耗散qutrit上得到验证，并在二维Fokker-Planck稳态上通过数值确认了完整链条。在高温和过阻尼极限下，量子公式退化为位置空间Fokker-Planck表达式，并以正确的温度因子重现Auconi的熵产生界。
英文摘要
In this paper, we study the quantum information-geometric structure underlying short-time nonequilibrium relaxation in quantum Markov dynamics, and derive bounds on the nonequilibrium correction to the short-time relaxation curvature. These bounds generalize the information-geometric structure underlying Auconi's classical nonequilibrium relaxation inequality to quantum Markov dynamics. We consider the von Neumann relative entropy as quantum divergence, and parametrize perturbations through the Kubo-Mori map, which converts the second-order expansion of the relative entropy into the Bogoliubov-Kubo-Mori (BKM) inner product at all temperatures. For a quantum Markov semigroup with full-rank stationary state, the induced tangent-space generator admits a canonical decomposition into a BKM-symmetric and a BKM-antisymmetric part, and the leading nonequilibrium curvature correction takes the exact form of the expectation of the commutator between the dissipative and the transport part of the generator. This correction is bounded by the product of a BKM-symmetric dissipative activity and a transport-sector activity. The bound is verified on a noncommuting qubit model and a driven-dissipative qutrit, and the full chain is confirmed numerically on a two-dimensional Fokker-Planck steady state. In the high-temperature and overdamped limit the quantum formula reduces to the position-space Fokker-Planck expression and reproduces Auconi's entropy-production bound with the correct temperature factor.
Comments11 pages
