Abstract In this paper, we extend the notion of non-microstate free entropy to the bi-free setting. Using a diagrammatic approach involving bi-non-crossing diagrams, bi-free difference quotients are constructed as analogues of the free partial derivations. Adjoints of bi-free difference quotients are discussed and used to define bi-free conjugate variables. Notions of bi-free Fisher information, non-microstate bi-free entropy, and non-microstate bi-free entropy dimension are defined and known properties in the free setting are extended to the bi-free setting.

中文翻译：

---

双自由概率论中熵的类比：非微观状态

摘要 在本文中，我们将非微态自由熵的概念扩展到双自由设置。使用涉及双非交叉图的图解方法，双自由差商被构造为自由部分推导的类似物。讨论了双自由差商的伴随并用于定义双自由共轭变量。定义了双自由 Fisher 信息、非微态双自由熵和非微态双自由熵维度的概念，并将自由设置中的已知属性扩展到双自由设置。