arXiv 0905.29182009-05physics.data-ancond-mat.stat-mechcs.CC

隐藏在复杂性度量背后的信息擦除

Information erasure lurking behind measures of complexity

Karoline Wiesner, Mile Gu, Elisabeth Rieper, Vlatko Vedral

备注：: Withdrawn: The main results, a corrected version of Theorem 1, and further results are contained in the new paper "Information-theoretic bound on the energy cost of stochastic simulation", http://arxiv.org/abs/1110.4217

摘要：

复杂系统存在于大多数科学分支中。如何最好地量化它们的复杂性以及达到什么目的仍然存在争议。一个重要的复杂性度量（统计复杂性）在预测系统行为所需的资源量方面具有操作意义。另一个（有效复杂度，又称过剩熵）是存储在系统中的互信息的度量。我们表明，对于任何给定的系统，这两种措施不同的预测过程中删除的信息量。我们将这种差异解释为给定模型的低效率。我们发现了一个约束的比率的两个措施定义为信息处理效率，类似于热力学第二定律。这两个重要的复杂性度量之间的新联系为复杂系统的好模型提供了一个定量标准，即那些几乎没有信息擦除的模型。

英文摘要：

Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the amount of resources needed to forecasting a system's behaviour. Another one (the effective measure complexity, aka excess entropy) is a measure of mutual information stored in the system proper. We show that for any given system the two measures differ by the amount of information erased during forecasting. We interpret the difference as inefficiency of a given model. We find a bound to the ratio of the two measures defined as information-processing efficiency, in analogy to the second law of thermodynamics. This new link between two prominent measures of complexity provides a quantitative criterion for good models of complex systems, namely those with little information erasure.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。