Anaya-Contreras Jorge A, Moya-Cessa Héctor M, Zúñiga-Segundo Arturo
Instituto Politécnico Nacional, ESFM Departamento de Física, Edificio 9 Unidad Profesional Adolfo López Mateos, 07738 México D.F., Mexico.
Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, 72840 Sta. María Tonantzintla, Pue., Mexico.
Entropy (Basel). 2019 Jan 10;21(1):49. doi: 10.3390/e21010049.
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.
荒木-利布不等式通常用于计算子系统最初处于纯态时的熵，因为这会迫使完整系统演化后两个子系统的熵相等。然后，通过求出小子系统的熵来计算大子系统的熵就很容易了。据我们所知，当其中一个子系统最初处于混合态时，不存在计算熵的方法。对于一个二能级原子与一个量子化场相互作用的情况，我们表明可以使用荒木-利布不等式并求出大（无限）系统的冯·诺依曼熵。我们在二能级原子-场相互作用中证明了这一点。
