发表机构
University of Cagliari（卡利亚里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文指出理想气体理论中热平衡与体积依赖熵存在公理矛盾，通过区分严格等温与准等温过程、引入伪等温过程概念修正熵的定义，发现热力学熵与统计微态计数是不同物理量，为经典热力学摆脱微观无序悖论提供了方法。
AI 中文摘要
对经典热力学的严格宏观分析揭示了理想气体理论基础中一处被忽视的矛盾：可逆等温过程中，熵的传统体积依赖公式违反了热平衡的基本公理。本文通过建立严格等温过程与准等温过程之间的严格操作区分，解决了这一不一致性。我们证明，为使理想气体完全符合经典热力学定律，其热力学熵必须仅是温度的函数。这种与体积无关的性质也通过对理想气体绝热自由膨胀的新分析得到证实，该过程被发现本质上是可逆的。为使这些结果与标准热力学实践相协调，我们引入了伪等温过程的概念（即由一系列小绝热和等容步骤组成的有限序列），并证明功和热的经典方程严格适用于这些实际过程，而非严格等温过程。最后，我们讨论了这些发现对统计力学的深远影响，表明修正后的热力学熵与麦克斯韦动理论完全一致，但与普朗克-玻尔兹曼公式存在本质差异。因此，热力学熵与统计微态计数是两种不同的物理量，本分析提供了一种将经典热力学从微观无序悖论中解放出来的简单方法。
英文摘要
A rigorous macroscopic analysis of classical thermodynamics reveals an overlooked contradiction at the foundations of ideal gas theory: the traditional volume dependent formula for entropy violates the fundamental axiom of thermal equilibrium during reversible isothermal processes. This paper resolves this inconsistency by establishing a strict operational distinction between strictly isothermal and quasi isothermal processes. We show that in order for the perfect gas to be strictly consistent with the laws of classical thermodynamics, the thermodynamic entropy of a perfect gas must be a function of temperature only. This independence of volume is also confirmed by a new analysis of the adiabatic free expansion of an ideal gas, which is found to be intrinsically reversible. To reconcile these results with standard thermodynamic practice, we introduce the concept of a pseudo isothermal process (a finite sequence of small adiabatic and isochoric steps) and show that the classical equations for work and heat apply rigorously to these real processes, as opposed to strictly isothermal ones. We conclude by discussing the profound implications of these findings for statistical mechanics, showing that while the corrected thermodynamic entropy is in perfect agreement with Maxwell's kinetic theory, it is essentially different from the Planck Boltzmann formula. Thus, thermodynamic entropy and statistical microstate counting are two different physical quantities, and the present analysis provides a simple way to free classical thermodynamics from the paradoxes of microscopic disorder.
Comments21 pages, 1 figure
