标题： 一种用于林德布洛德方程的熵梯度结构以及量子系统与宏观模型耦合的GENERIC形式 显示英文标题

标题： An entropic gradient structure for Lindblad equations and GENERIC for quantum systems coupled to macroscopic models

摘要： 我们证明了在有限维希尔伯特空间上满足热平衡态详细平衡条件的所有林德布拉德算子（即量子半群的生成元）都可以相对于相对熵写成梯度系统。我们还讨论了与宏观系统的热力学一致耦合，既可以作为恒定温度的阻尼哈密顿系统，也可以作为GENERIC系统。 显示英文摘要

摘要： We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finite-dimensional Hilbert space satisfying the detailed balance condition with respect to the thermal equilibrium state can be written as a gradient system with respect to the relative entropy. We discuss also thermodynamically consistent couplings to macroscopic systems, either as damped Hamiltonian systems with constant temperature or as GENERIC systems.