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Abstract：
The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki-Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.
摘要：
Araki-Lieb不等式通常用于计算子系统最初处于纯状态时的熵，因为这迫使两个子系统的熵在整个系统进化后相等。然后，通过找到小子系统的熵，很容易计算大子系统的熵。据我们所知,当一个子系统最初处于混合状态时，不存在计算熵的方法。对于两级原子与量化场相互作用的情况，我们证明了可以使用Araki-Lieb不等式并找到大型（无限）系统的vonNeumann熵。我们在两级原子-场相互作用中证明了这一点。
