发表机构
Universidad Metropolitana de Ciencias de la Educación; Université Libre de Bruxelles; International SOLVAY Institutes for Physics and Chemistry（大都会教育科学大学; 布鲁塞尔自由大学; 国际索尔维物理与化学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过对比理想气体自由膨胀与自引力系统收缩，用基础热力学论证阐明熵增与空间分散并非必然对应，并扩展到黑洞与霍金辐射，为教学提供桥梁。
AI 中文摘要
在大学物理课程中一个值得讨论的有趣问题是引力是否可能与热力学第二定律相冲突。在本工作中，我们通过比较理想气体在两种概念上不同的状态下的行为来探讨这一问题：一种是可以忽略引力效应的状态，另一种是自引力变得重要的状态。在第一种情况下，自由膨胀提供了熟悉的例子，即气体可达到的体积增加导致熵增加。自引力系统则表现不同：引力收缩可以减少物质所占的体积，同时释放能量并增加周围环境的熵。这说明了为什么通常认为熵增加必然对应空间分散度增加的直觉不能直接应用于自引力系统。利用基本的热力学论证和最少的数学，我们讨论了这一表面上的张力，并展示了如何必须考虑包括发射辐射在内的完整系统的熵。讨论最终扩展到黑洞和霍金辐射，其中适当的框架是广义热力学第二定律。该分析旨在为基本热力学与引力系统的一些独特热力学性质之间提供一座教学桥梁。
英文摘要
An interesting question for discussion in university physics courses is whether gravity can conflict with the second law of thermodynamics. In this work, we address this question by comparing the behavior of an ideal gas in two conceptually different regimes: one in which gravitational effects can be neglected and another in which self-gravity becomes important. In the first case, free expansion provides the familiar example in which an increase in the volume accessible to the gas leads to an increase in entropy. Self-gravitating systems behave differently: gravitational contraction can reduce the volume occupied by matter while releasing energy and increasing the entropy of the surroundings. This illustrates why the usual intuition that increasing entropy necessarily corresponds to increasing spatial dispersion cannot be applied directly to self-gravitating systems. Using elementary thermodynamic arguments and a minimal amount of mathematics, we discuss this apparent tension and show how entropy must be considered for the complete system, including emitted radiation. The discussion is finally extended to black holes and Hawking radiation, where the appropriate framework is the generalized second law of thermodynamics. The analysis is intended to provide a pedagogical bridge between elementary thermodynamics and some of the distinctive thermodynamic properties of gravitating systems.
Comments9 pages, 4 figures
