For non-equilibrium quasi-stationary-states (QSS), we present a theoretical background based on a family of Vlasov equation solutions constructed by non-Gaussian distributions. Proposing a transformation, we connect the Vlasov stationary solutions to a non-standard theoretical perspective. Such one is suitable to describe the QSS involved in the d-HMF model, which occur while the system evolves towards equilibrium. Our results complement the notion of Tsallis formalism and represent input on a theoretical description of the systems behavior with long-range interactions out of equilibrium.

中文翻译：

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基于一族Vlasov解的偶极型哈密顿平均场模型的准平稳态的统计描述

对于非平衡准平稳态（QSS），我们提出了基于非高斯分布构造的Vlasov方程解族的理论背景。建议进行转换，我们将Vlasov平稳解与非标准理论观点联系起来。这样的描述适合描述d-HMF模型中涉及的QSS，它是在系统趋于平衡时发生的。我们的结果补充了Tsallis形式主义的概念，并代表了系统行为的理论描述，其中系统行为具有长期的不平衡性。