Plastino Angelo, Rocca Mario Carlos, Pennini Flavia
Consejo Nacional de Investigaciones Científicas y Tecnológicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina.
Departamento de Física, Universidad Nacional de La Plata, 1900 La Plata, Argentina.
Entropy (Basel). 2020 Apr 24;22(4):491. doi: 10.3390/e22040491.
There are entropic functionals galore, but not simple objective measures to distinguish between them. We remedy this situation here by appeal to Born's proposal, of almost a hundred years ago, that the square modulus of any wave function | ψ | 2 be regarded as a probability distribution . the usefulness of using information measures like Shannon's in this pure-state context has been highlighted in [, , 446]. Here we will apply the notion with the purpose of generating a dual functional [ F α R : { S Q } ⟶ R + ], which maps entropic functionals onto positive real numbers. In such an endeavor, we use as standard ingredients the coherent states of the harmonic oscillator (CHO), which are unique in the sense of possessing minimum uncertainty. This use is greatly facilitated by the fact that the CHO can be given analytic, compact closed form as shown in [ , , 191]. Rewarding insights are to be obtained regarding the comparison between several standard entropic measures.
熵泛函有很多，但没有简单的客观方法来区分它们。我们通过诉诸近百年前玻恩的提议来解决这一情况，即任何波函数(\vert\psi\vert^2)的平方模应被视为概率分布。在这种纯态背景下使用诸如香农信息测度的有用性已在[参考文献]中得到强调。在这里，我们将应用这一概念，目的是生成一个对偶泛函([F_{\alpha R}:{S_Q}\to\mathbb{R}^+])，它将熵泛函映射到正实数上。在这样的努力中，我们使用谐振子的相干态（CHO）作为标准要素，它们在具有最小不确定性的意义上是独特的。正如[参考文献]所示，CHO可以用解析的、紧凑的封闭形式给出，这极大地便利了这种使用。关于几种标准熵测度之间的比较将获得有价值的见解。
