有限非平衡统计热力学的基础：外延量
Foundations of a Finite Non-Equilibrium Statistical Thermodynamics: Extrinsic Quantities
AI总结：
本文针对统计热力学基础的长期争议，构建有限非平衡系统统计热力学框架，修正吉布斯熵公式解释熵增，解决多个经典佯谬，并通过扩散理想气体验证外延量的平衡一致性。
摘要：
统计热力学作为一种塑造我们对平衡热力学态认知的概念框架，具有重要价值。然而，围绕该理论基础存在的大量未解决问题，可能会让中立的观察者认为统计热力学正处于危机之中。事实上，科学界关于不可逆性微观起源的讨论已经持续了一百多年。本文在探讨这些问题的同时，着手构建适用于有限非平衡系统的统计热力学。研究为基本热力学关系中的所有外延变量提出了定义，这些定义与平衡热力学极限下的现有结果保持一致。相空间上的概率密度函数被解释为对微观态的主观不确定性，同时对吉布斯熵公式进行了修正，使得在无需引入额外物理规律或修改相空间动力学的前提下，能够解释熵的产生。针对混合佯谬、吉布斯佯谬、洛施密特佯谬以及麦克斯韦妖思想实验，本文提出了相应的解决方案。最后，研究计算了扩散理想气体中基本热力学关系的外延量随时间和空间的变化函数，并证明在经典语境下解读时，其初始值和终值与预期的平衡值一致。
英文摘要：
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to conclude that statistical thermodynamics is in a state of crisis though. Indeed, the discussion about the microscopic origins of irreversibility has continued in the scientific community for more than a hundred years. This paper considers these questions while beginning to develop a statistical thermodynamics for finite non-equilibrium systems. Definitions are proposed for all of the extrinsic variables of the fundamental thermodynamic relation that are consistent with existing results in the equilibrium thermodynamic limit. The probability density function on the phase space is interpreted as a subjective uncertainty about the microstate, and the Gibbs entropy formula is modified to allow for entropy creation without introducing additional physics or modifying the phase space dynamics. Resolutions are proposed to the mixing paradox, Gibbs' paradox, Loschmidt's paradox, and Maxwell's demon thought experiment. Finally, the extrinsic variables of the fundamental thermodynamic relation are evaluated as functions of time and space for a diffusing ideal gas, and the initial and final values are shown to coincide with the expected equilibrium values when interpreted in a classical context.
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