We demonstrate the concavity of the Tsallis entropy along the heat flow for general dimensions, expanding upon the findings of Wu et al 2025 and Hung 2022, which were previously limited to the one-dimensional case. The core of the proof is a novel estimate of the terms in the second-order time derivative, and a rigorous validation of integration by parts. The resulting bound establishes a new functional inequality, which may be of interest for other areas of mathematical analysis.

翻译：我们证明了在一般维度下Tsallis熵沿热流的凹性，拓展了Wu等人2025年和Hung 2022年的研究成果——此前该结论仅在一维情形下成立。证明的核心在于对二阶时间导数项的新颖估计，以及分部积分法的严格验证。由此得到的界建立了一个新的函数不等式，该不等式可能对数学分析的其他领域具有研究价值。