In an attempt to find the dynamical foundations for q-entropies, we examine the special case of Lagrangian/Hamiltonian systems of many degrees of freedom whose statistical behavior is conjecturally described by the q-entropic functionals. We follow the spirit of the canonical ensemble approach. We consider the system under study as embedded in a far larger total system. We explore some of the consequences that such an embedding has, if it is modeled by a Riemannian submersion. We point out the significance in such a description of the finite-dimensional Bakry–Émery Ricci tensor, as a local mesoscopic invariant, for understanding the collective dynamical behavior of systems described by the q-entropies.

中文翻译：

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q-熵的黎曼浸没

试图找到动力基础q-熵，我们检查了具有许多自由度的拉格朗日/哈密顿系统的特殊情况，其统计行为由q-熵泛函。我们遵循规范集成方法的精神。我们认为正在研究的系统嵌入在一个更大的总系统中。如果使用黎曼浸没对其进行建模，我们将探讨这种嵌入所产生的一些后果。我们指出了将有限维 Bakry-Émery Ricci 张量作为局部介观不变量的这种描述对于理解由q-熵。