AI 中文总结
该研究提出热力学第二定律可从宏观态概率与微观态数的正相关及相空间连续性方程自然导出，明确其统计本质，同时指出局部非混沌系统中该正相关可能失效，传统热力学框架不再适用，熵可自发减小。
AI 中文摘要
热力学第二定律目前仍缺乏适用于经典和量子系统、覆盖广泛时间尺度、相互作用类型及非平衡程度的通用证明。本文表明，当孤立系统的宏观态概率$f$随可能微观态数目$Ω$单调递增（即$\frac{\text{d}f}{\text{d}Ω}>0$）时，第二定律可从相空间中$f$的连续性方程自然导出；$\frac{\text{d}f}{\text{d}Ω}>0$的一个特例是玻尔兹曼的平衡态先验等概率假设。基于这一发现，可轻松推导出完全混沌系统的第二定律，该推导不依赖动力学细节，凸显了熵增的统计本质。与之相对，对于局部非混沌系统，$f$与$Ω$之间的正相关可能被打破（即$\frac{\text{d}f}{\text{d}Ω}\text{≤}0$），此时传统热力学框架不再适用，熵可在无任何能量代价的情况下自发减小。
英文摘要
The second law of thermodynamics still lacks a general proof applicable to both classical and quantum systems across broad ranges of time scales, interactions, and degrees of nonequilibrium. In this paper, we show that when the macrostate-level probability $f$ of an isolated system increases monotonically with the number of possible microstates $Ω$ (i.e., $\partial f/\partial Ω> 0$), the second law emerges naturally from the continuity equation of $f$ in phase space; a special case of $\partial f/\partial Ω> 0$ is Boltzmann's assumption of equal a priori equilibrium probabilities. Based on this finding, the second law can be readily derived for fully chaotic systems. The derivation does not rely on dynamical details, highlighting the statistical nature of entropy increase. In contrast, for a locally nonchaotic system, the positive correlation between $f$ and $Ω$ may break down (i.e., $\partial f/\partial Ω\leq 0$). Consequently, the conventional framework of thermodynamics does not apply, and entropy can decrease spontaneously without any energetic penalty.
Comments33 pages, 7 figures
