发表机构
University of Campania “Luigi Vanvitelli”; Institute for Complex Systems, CNR; Università di Padova; Università Sapienza; University of Rome “La Sapienza”（坎帕尼亚路易吉·范维特利大学; 意大利国家研究委员会复杂系统研究所; 帕多瓦大学; 罗马智慧大学; 罗马第一大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于辛钦观点，通过谐振子链和Toda模型等可积系统的解析与数值结果，论证统计力学有效性仅需大自由度和广延可观测量，无需动力学混沌，并观察到麦克斯韦-玻尔兹曼分布等平衡特征。
AI 中文摘要
最初由吉布斯提出的基于系综的统计力学表述，在描述多粒子系统的平衡态方面已被证明极其有效，其应用涵盖了最广泛的背景（仅举几例：临界现象、量子力学、生物物理学）。这一成功的原因至今仍有争议，大系统中动力学与概率之间的联系在某种程度上仍然难以捉摸。实际上，为了推导平衡统计力学的主要结果，通常需要对动力学的遍历性做出强假设。尽管如此，经验观察似乎表明，即使在这些假设未被验证的情况下，理论的预测仍然成立。在本文中，我们重新审视了辛钦提出的观点，该观点指出，统计力学有效性的唯一相关要素是系统中大量的自由度以及对广延可观测量（extensive observables）的选择，而与微观动力学的细节无关。特别是，动力学混沌的存在并非必需。为此，我们讨论了一对经典可积系统——谐振子链（harmonic chain）和Toda模型——上的一些解析和数值结果，表明平衡统计力学预测的许多重要特征，例如麦克斯韦-玻尔兹曼分布，即使在无混沌的情况下也能被观察到。
英文摘要
The formulation of statistical mechanics in terms of ensembles, originally proposed by Gibbs, has proved to be extremely effective in describing the equilibrium state of many-particle systems, in the most diverse contexts (critical phenomena, quantum mechanics, biophysics, just to mention a few). The reasons of this success are still debated, and the connection between dynamics and probability in large systems remains somehow elusive. Indeed, in order to derive the main results of equilibrium statistical mechanics, strong assumptions on the ergodicity of the dynamics are usually required. Nonetheless, empirical observations seem to suggest that the predictions of the theory hold true even when such assumptions are not verified. In this paper we reconsider the point of view put forward by Khinchin, stating that the only relevant ingredients for the validity of statistical mechanics are the large number of degrees of freedom in the system and the choice of extensive observables, irrespectively of the details of the microscopic dynamics. In particular, the presence of dynamical chaos is not required. To this aim, we discuss some analytical and numerical results on a couple of classical integrable systems, the harmonic chain and the Toda model, showing that many important features predicted by equilibrium statistical mechanics, as for instance Maxwell-Boltzmann distribution, are found even in absence of chaos.
Comments12 pages, 7 figures
Journal refPhilosophical Transactions of the Royal Society A (2026)
