标题： 准粒子的统计力学 显示英文标题

标题： Statistical Mechanics of Paraparticles

摘要： 量子力学大致将粒子分为两类：$(1)$费米子和$(2)$玻色子。 费米子是半整数自旋粒子，遵循泡利不相容原理和费米-狄拉克统计。 而玻色子是整数自旋粒子，不遵循泡利不相容原理，遵循玻色-爱因斯坦统计。 然而，这一标准情况有两个例外：第一，任何子，它存在于二维系统中；第二，次粒子，它可以存在于任何维度中。 次粒子遵循其非平凡的次统计，遵循其广义的不相容原理。 在本文中，我们对\cite{wang2025particle}中建立的次粒子统计基础进行了详细综述。 我们进一步扩展了这项工作，然后推导出一个特定情况下次粒子热容量的重要表达式，这将为在适当系统中实验检测次粒子提供手段。 显示英文摘要

摘要： Quantum mechanics broadly classifies the particles into two categories: $(1)$ fermions and $(2)$ bosons. Fermions are half-integer spin particles, obeying Pauli's exclusion principle and Fermi-Dirac statistics. Whereas bosons are integer spin particles, not obeying Pauli's exclusion principle, and obeying Bose-Einstein statistics. However, there are two exceptions to this standard case: first, anyons, which exist in 2-dimensional systems, and secondly, paraparticles, which can exist in any dimension. Paraparticles follow their non-trivial parastatistics, obeying their generalised exclusion principle. In this paper, we provide a detailed review of the foundations of paraparticle statistics established in \cite{wang2025particle}. We extend this work further and then derive an important expression for the heat capacity of paraparticles for a specific case, which would provide a handle for the experimental detection of paraparticles in appropriate systems.