The similarity principle is an extension of the principle of thermal relaxation that naturally arises in the stochastic limit of quantum theory. We construct examples of Low Density Limit (LDL) generators, associated to an environment state in equilibrium at inverse temperature β, which admit non-(β, H_S)-equilibrium states. We prove that in some cases, the attraction domain of the (β, H_S)-equilibrium state is empty. This means that the similarity principle, in its original thermodynamical formulation, can be broken in the LDL limit. This result is obtained as a consequence of a more general phenomenon: the role of degeneracies in the spectrum of the Liouvillian of the system Hamiltonian associated to the generator. We start from the definition of LDL type generators given in [5] and we introduce a finer classification of these generators based on the above degeneracies. The simplest subclass, called 2-generic, is a nontrivial extension of the generators associated to the so-called Λ and V configurations, widely used in quantum optics and involving 2 levels of the system Hamiltonian. Since each 2-generic block involves 3 or 4 levels of the system Hamiltonian we expect that they can reveal some interesting new physical phenomenon, as it happened in the 2-level case. In the last section, we restrict our attention to a 3-level system with a Hamiltonian that is associated to a class of 2-generic LDL generators. Finally, we prove that, for some LDL generators in this class the statement formulated at the beginning holds true.

中文翻译：

---

打破低密度极限型马尔可夫生成元中的相似性原理以及简并在不变状态景观中的作用

这相似原则是原理的延伸热弛豫这自然出现在量子理论的随机极限中。我们构建了低密度极限 (LDL) 发生器的示例，这些发生器与在反温度下处于平衡状态的环境状态相关联β，其中承认非（β,H_小号)-平衡状态。我们证明在某些情况下，(β,H_小号)-平衡状态为空。这意味着在其原始热力学公式中的相似性原理可以在 LDL 限制中被打破。这个结果是作为一个更普遍现象的结果得到的：简并在与生成器相关的系统哈密顿量的刘维利安谱中的作用。我们从 [5] 中给出的 LDL 类型生成器的定义开始，并根据上述退化对这些生成器进行更精细的分类。最简单的子类，称为 2-通用的, 是与所谓的 Λ 和五配置，广泛用于量子光学并涉及系统哈密顿量的2个级别。由于每 2-通用的块涉及系统哈密顿量的 3 或 4 个级别，我们希望它们可以揭示一些有趣的新物理现象，就像在 2 级情况下发生的那样。在最后一节中，我们将注意力限制在一个具有哈密顿量的 3 级系统上，该系统与一类 2 泛型 LDL 生成器相关联。最后，我们证明，对于该类中的一些 LDL 生成器，开始制定的陈述是正确的。