热力学的普遍基础：熵与能量超越平衡与非扩展性
Universal Foundations of Thermodynamics: Entropy and Energy Beyond Equilibrium and Without Extensivity
AI总结：
本文提出热力学普遍基础，定义熵与能量超越平衡与非扩展性，通过能量-熵图示分析非平衡系统，推导克劳修斯不等式并拓展第二定律至非平衡过程。
摘要：
热力学通常被描述为稳定平衡宏观系统的理论，基于扩展性和系统大小的假设。本文提出热力学基本原理的普遍表述，其中熵和能量定义和应用超越平衡且不假设扩展性。该表述适用于所有系统，无论大小、粒子数量多少，以及所有状态，无论是平衡还是非平衡状态，通过精心陈述的操作定义和存在原理而非宏观理想化。关键热力学概念，包括绝热可用性和可用能量，通过能量-熵图示非平衡状态的表示进行开发和示例，提供对不可逆性和工作提取限制的几何洞察。本文大部分内容致力于分析非工作相互作用中的熵转移，导致对热相互作用和热-扩散相互作用的精确定义，这对简单和复杂固体和流体的非平衡行为的介观连续理论至关重要。作为此分析的直接结果，克劳修斯不等式和克劳修斯第二定律陈述以明确扩展到非平衡过程的形式被推导出来。由此产生的框架将热力学呈现为适用于所有系统的普遍理论，无论大小，并为教学和现代应用提供一致的基础。
英文摘要：
Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary foundations of thermodynamics, in which entropy and energy are defined and employed beyond equilibrium and without assuming extensivity. The formulation applies to all systems -- large and small, with many or few particles -- and to all states, whether equilibrium or nonequilibrium, by relying on carefully stated operational definitions and existence principles rather than macroscopic idealizations. Key thermodynamic concepts, including adiabatic availability and available energy, are developed and illustrated using the energy-entropy diagram representation of nonequilibrium states, which provides geometric insight into irreversibility and the limits of work extraction for systems of any size. A substantial part of the paper is devoted to the analysis of entropy transfer in non-work interactions, leading to precise definitions of heat interactions and heat-and-diffusion interactions of central importance in mesoscopic continuum theories of nonequilibrium behavior in simple and complex solids and fluids. As a direct consequence of this analysis, Clausius inequalities and the Clausius statement of the second law are derived in forms explicitly extended to nonequilibrium processes. The resulting framework presents thermodynamics as a universal theory whose concepts apply uniformly to all systems, large and small, and provides a coherent foundation for both teaching and modern applications.
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