AI 中文总结
研究在洛伦兹瑞查杜里方程与佩雷尔曼非坍缩定理间建立对应，通过解释方程为里奇流类似物，导出洛伦兹非坍缩定理与协变熵泛函，提出测地线熵容量概念，构建引力、热力学和信息统一几何框架。
AI 中文摘要
本文在洛伦兹瑞查杜里方程与里奇流的佩雷尔曼非坍缩定理之间建立了几何对应关系。将瑞查杜里方程解释为里奇流的洛伦兹类似物，把广义相对论中的测地线聚焦与几何分析的单调性和熵泛函联系起来。利用此对应关系导出洛伦兹非坍缩定理并引入控制因果体积演化的协变熵泛函。最后提出测地线熵容量概念，为引力、热力学和信息提供统一几何框架。
英文摘要
In this paper, we establish a geometric correspondence between the Lorentzian Raychaudhuri equation and Perelman's non-collapsing theorem for the Ricci flow. By interpreting the Raychaudhuri equation as a Lorentzian analogue of Ricci flow, we connect geodesic focusing in general relativity to the monotonicity and entropy functionals of geometric analysis. Using this correspondence, we derive a Lorentzian non-collapsing theorem and introduce a covariant entropy functional governing causal volume evolution. Finally, we propose the concept of geodesic entropy capacity, a curvature-bounded limit on the information that can be stored in spacetime regions, providing a unified geometric framework linking gravitation, thermodynamics, and information.
CommentsWe establish, using comparison geometry, a finite entropy bound below a critical threshold and prove that the corresponding geometric evolution remains smooth for all proper times for which the entropy stays below the critical value. The paper contains one theorem, proof, and references
Journal refPhysics Letters B Date: April 2026 Article: 140355 Volume: Volume 875
DOI：10.1016/j.physletb.2026.140355
