In recent previous work, the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this paper, the approach is generalized to systems defined by more than one Hamiltonian constraint (multi-fingered time). We show how well-known features as the Ehrenfest–Tolman effect and the Jüttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the definition of a global notion of equilibrium is discussed.

中文翻译：

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多指时间协变系统的统计力学

在最近的先前工作中，作者提出了一种新的方法，将统计力学的框架扩展到无需额外计量器的重新参数化不变系统。在本文中，该方法被推广到由多个哈密顿约束（多指时间）定义的系统。我们展示了如何从多指框架的协变方法中一致地恢复出著名的特征，如埃伦菲斯特-托尔曼效应和相对论气体的尤特纳分布。最终，讨论了相互作用在整体均衡概念的定义中所起的关键作用。