数字相空间中弹性粒子的统计原理
The statistical principle of elastic particles in digital phase space
通过引入路程子空间，本项研究将能量相空间扩展为数字相空间（$\Lambda$ 空间），从而完成了弹性粒子平衡系统的数字化统计。不同于吉布斯统计系综的$\Gamma$相空间（6N维），$\Lambda$ 相空间（18N 维）分为液体、固体和气体三个区域，其能量概率分布函数具有循环对称性。$\Lambda$ 空间采用缔合度表征粒子相互作用，从而避免了$\Gamma$空间的势能积分难题。本文给出了弹性粒子系统的宏观和介观平衡条件，导出了三个区域的配分函数和状态函数。此外，通过扩展熵函数的定义，将热力学微分方程推广到全物态范围。结果表明，物质的结构信息可以利用四个独立的参数进行解码：一个数字变量和三个标度基。
物理学
统计物理弹性粒子统计相空间配分函数热力学方程物质结构
梁忠诚.数字相空间中弹性粒子的统计原理[EB/OL].(2025-08-17)[2025-10-23].https://chinaxiv.org/abs/202508.00249.点此复制
By introducing the path subspace, this study extends the energy phase space to a digital phase space ($\Lambda$-space), thus accomplishing the digital statistics of the elastic particle equilibrium systems. Unlike the $\Gamma$ phase space (6N dimensions) of Gibbs statistical ensemble, the $\Lambda$-space (18N dimensions) is divided into three regions: liquid, solid, and gas, and their energy probability distributions have cyclic symmetry. The interaction between particles in $\Lambda$-space is characterized by the degree of association, thereby avoiding the problem of potential energy integration in $\Gamma$-space. This article presents the macroscopic and mesoscopic equilibrium conditions for elastic particle systems and derives the partition functions and state functions for three regions. In addition, the thermodynamic differential equations are generalized to the entire range of matter states by extending the definition of the entropy function. The results indicate that the structural information of matter can be decoded using four independent parameters: one digital variable and three scale bases.
statistical physicselastic particlesstatistical phase spacepartition functionthermodynamic functionsstructure of matter
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