Entanglement is at the core of quantum physics, playing a central role in quantum phenomena involving composite systems. According to the timeless picture of quantum dynamics, entanglement may also be essential for understanding the very origins of dynamical evolution and the flow of time. Within this point of view, the Universe is regarded as a bipartite entity comprising a clock $C$ and a system $R$ (or “rest of the Universe”) jointly described by a global stationary state, and the dynamical evolution of $R$ is construed as an emergent phenomena arising from the entanglement between $C$ and $R$. In spite of substantial recent efforts, many aspects of this approach remain unexplored, particularly those involving mixed states. In the present contribution we investigate the timeless picture of quantum dynamics for mixed states of the clock-system composite, focusing on quantitative relations linking the clock-system entanglement with the emerging dynamical evolution experienced by the system.

中文翻译：

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纠缠混合态的新兴动力学

纠缠是量子物理学的核心，在涉及复合系统的量子现象中起着核心作用。根据对量子动力学的永恒描述，纠缠对于理解动力学演化和​​时间流逝的起源也可能是必不可少的。在这种观点下，宇宙被视为包括时钟的两部分实体$C$ 和一个系统 $\mathrm{[R}$ （或“宇宙的其余部分”）共同描述为一个整体的静止状态，以及 $\mathrm{[R}$ 被解释为由于 $C$ 和 $\mathrm{[R}$。尽管最近做出了巨大努力，但该方法的许多方面仍未得到探索，尤其是涉及混合国家的方面。在当前的贡献中，我们研究了时钟系统复合物混合状态的量子动力学的永恒画面，重点是将时钟系统纠缠与系统所经历的新兴动力学演化联系起来的定量关系。