Deformations of geometric characteristics of statistical hypersurfaces governed by the law of growth of entropy are studied. Both general and special cases of deformations are considered. The basic structure of the statistical hypersurface is explored through a differential relation for the variables, and connections with the replicator dynamics for Gibbs’ weights are highlighted. Ideal and super-ideal cases are analyzed, while considering their integral characteristics.

中文翻译：

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统计超曲面的熵驱动变换

研究了由熵增长规律控制的统计超曲面几何特征的变形。考虑了变形的一般和特殊情况。通过变量的微分关系探索了统计超曲面的基本结构，并强调了与 Gibbs 权重的复制器动力学的联系。分析了理想和超理想情况，同时考虑了它们的整体特征。