We define the uniform and completely nonequilibrium invariant states, which are associated with Eulerian cycles; once we did this, we use the Hierholzer’s algorithm to obtain a canonical Euler-Hierholzer cycle, and for it, characterize the invariant state. For the simplest case of nonequilibrium, we give sufficient conditions for these states to be invariant and write its eigenvalues explicitly.

中文翻译：

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与欧拉循环相关的弱耦合极限型量子马尔可夫半群的均匀和完全非平衡不变态

我们定义了与欧拉循环相关的均匀且完全非平衡不变的状态；一旦我们这样做了，我们就使用 Hierholzer 算法来获得一个规范的 Euler-Hierholzer 循环，并为此表征不变状态。对于最简单的非平衡情况，我们给出了使这些状态保持不变的充分条件，并明确地写出其特征值。