微分熵与时间
Differential entropy and time
摘要：
我们给出了一个详细的吉布斯型熵的概念和它的动力学行为的情况下，依赖于时间的连续概率分布的不同来源：相关的经典和量子系统。在非平衡Smoluchowski过程的情况下，条件Kullback-Leibler和Gibbs（Shannon）熵的目的依赖的使用被解释。吉布斯熵和库尔贝克熵的一个非常不同的时间行为面临。一个特定的概念利基解决，量子冯诺依曼，经典的Kullback-Leibler和吉布斯熵可以始终作为同一物理系统的信息措施。如果概率密度的动力学是由薛定谔图像波包演化驱动的，吉布斯型和相关的费舍尔信息泛函似乎可以量化平均值中的非平凡功率传输过程。这一观察结果被发现扩展到经典的耗散过程，并支持这样的观点，即香农熵动力学提供了一个洞察物理相关的非平衡现象，这是不可访问的Kullback-Leibler熵，通常在文献中被忽略。
英文摘要：
We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage of conditional Kullback-Leibler and Gibbs (Shannon) entropies is explained in case of non-equilibrium Smoluchowski processes. A very different temporal behavior of Gibbs and Kullback entropies is confronted. A specific conceptual niche is addressed, where quantum von Neumann, classical Kullback-Leibler and Gibbs entropies can be consistently introduced as information measures for the same physical system. If the dynamics of probability densities is driven by the Schrödinger picture wave-packet evolution, Gibbs-type and related Fisher information functionals appear to quantify nontrivial power transfer processes in the mean. This observation is found to extend to classical dissipative processes and supports the view that the Shannon entropy dynamics provides an insight into physically relevant non-equilibrium phenomena, which are inaccessible in terms of the Kullback-Leibler entropy and typically ignored in the literature.
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