Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand, Suzuki proposes an exact equality for quantum systems. In this paper, we discuss the relation between the two results and in particular, look for the analogue of the Suzuki result for classical systems. This requires us to examine as to what constitutes a complete set of conserved quantities required to saturate the Mazur bound. We present analytic arguments as well as illustrative numerical results from a number of different systems. Our examples include systems with few degrees of freedom as well as many-particle integrable models, both free and interacting.

Mazur界和Suzuki相等性是对时间依赖的平衡相关性已知的为数不多的严格结果，对于理解输运性质很重要。在涉及守恒量的平衡相关函数方面，Mazur不等式在可观察物的时间相关自相关函数的长期平均值上给出了一个下限。另一方面，铃木提出了量子系统的精确等式。在本文中，我们讨论了两个结果之间的关系，尤其是寻找经典系统中Suzuki结果的类似物。这就要求我们检查什么构成了使Mazur界饱和的守恒量的完整集合。我们提供了来自许多不同系统的解析论证以及示例性数值结果。