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arXiv 1401.7997quant-phcond-mat.stat-mech
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相对热化

Relative Thermalization

Lidia del Rio, Adrian Hutter, Renato Renner, Stephanie Wehner

备注：
8 + 19 pages, 6 figures
发表信息：
Phys. Rev. E 94, 022104 (2016)
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摘要：

当研究量子系统的热化时，通常会问与环境相互作用的系统是否会朝着局部热态演化。在这里，我们表明，一个更普遍和相关的问题是“当一个系统热化相对于一个特定的参考？“相对热化是指，除了处于局部热状态外，系统与参考不相关。我们认为，这是必要的，以适用于标准的统计力学的研究之间的相互作用的热化系统和参考。然后，我们推导出与任意环境相互作用的量子系统的相对热化的条件。这个条件有两个组成部分：第一个是状态无关的，反映了不变子空间的结构，如能量壳，以及系统和环境的相对大小;第二个依赖于参考，系统和环境之间的初始相关性，用条件熵来衡量。直观地说，与大环境相互作用的小系统可能会相对于参考发生热化，但前提是参考最初与系统和环境不高度相关。我们的陈述使这种直觉精确，我们表明，在许多自然环境中，这种热化条件近似紧。建立热化的结果，通常忽略了参考，遵循我们的声明的特殊情况。

英文摘要：

When studying thermalization of quantum systems, it is typical to ask whether a system interacting with an environment will evolve towards a local thermal state. Here, we show that a more general and relevant question is "when does a system thermalize relative to a particular reference?" By relative thermalization we mean that, as well as being in a local thermal state, the system is uncorrelated with the reference. We argue that this is necessary in order to apply standard statistical mechanics to the study of the interaction between a thermalized system and a reference. We then derive a condition for relative thermalization of quantum systems interacting with an arbitrary environment. This condition has two components: the first is state-independent, reflecting the structure of invariant subspaces, like energy shells, and the relative sizes of system and environment; the second depends on the initial correlations between reference, system and environment, measured in terms of conditional entropies. Intuitively, a small system interacting with a large environment is likely to thermalize relative to a reference, but only if, initially, the reference was not highly correlated with the system and environment. Our statement makes this intuition precise, and we show that in many natural settings this thermalization condition is approximately tight. Established results on thermalization, which usually ignore the reference, follow as special cases of our statements.

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