AI 中文总结
研究斯奈德和斯奈德 - 德西特非对易背景下爱因斯坦晶体行为，在热力学框架内分析新效应，发现非对易性影响内能和比热等关键热力学量，且与GUP、GEUP类型的不确定性关系修改相关。
AI 中文摘要
我们研究了由斯奈德和斯奈德 - 德西特模型描述的非对易背景下爱因斯坦晶体的行为。在热力学框架内分析了可能出现在诸如钻石晶体等现实系统中的新效应。我们表明非对易性影响关键热力学量，包括内能和比热。这些修正可直接与广义不确定性原理（GUP）和广义扩展不确定性原理（GEUP）类型的基础不确定性关系的修改相关。
英文摘要
We investigate the behavior of Einstein crystals in noncommutative backgrounds described by the Snyder and Snyder-de Sitter models. Possible novel effects, which may arise in realistic systems such as diamond crystals, are analyzed within a thermodynamical framework. We show that noncommutativity influences the key thermodynamic quantities, including internal energy and specific heat. These corrections can be directly related to modifications of the underlying uncertainty relations, of the generalized uncertainty principle (GUP) and generalized extended uncertainty principle (GEUP) types.
Comments10 pages, published version
Journal refPhys.Rev.D 113 (2026) 11, 116028
