近日，奥地利维也纳工业大学的Stefan Rotter及其研究小组与法国蔚蓝海岸大学的Ulrich Kuhl等人合作并取得一项新进展。经过不懈努力，他们对波散射中费雪信息流的连续性方程进行研究。相关研究成果已于2024年6月10日在国际知名学术期刊《自然—物理学》上发表。

该研究团队证明了电磁波散射在一个物体上，携带了关于物体所有本构参数的局部定义和保守信息。具体而言，研究人员引入针对一般类型波场的费雪信息的密度和通量，并确定了相应的信息源和信息汇，通过这些信息源和信息汇，所有这些新量都满足基本连续性方程。研究人员通过一项实验，成功验证了他们的理论预测。

在实验中，他们研究了嵌入在无序环境中的可移动物体，并准确测量了微波频率下的费雪信息通量。这项研究结果提高了对信息生成和传播的理解，并为跟踪和设计即使在复杂环境中的信息流开辟了可能性。

据悉，从地震学到雷达技术，从生物医学成像到精密测量，利用波来探索我们的环境是一种广泛使用的范例。在所有这些领域中，中心目标都是通过向感兴趣的对象发送探测波，并处理传递回探测器的信息来收集尽可能多的信息。

附：英文原文

Title: Continuity equation for the flow of Fisher information in wave scattering

Author: Hupfl, Jakob, Russo, Felix, Rachbauer, Lukas M., Bouchet, Dorian, Lu, Junjie, Kuhl, Ulrich, Rotter, Stefan

Issue&Volume: 2024-06-10

Abstract: Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from biomedical imaging to precision measurements. In all these fields, the central aim is to gather as much information as possible about an object of interest by sending a probing wave at it and processing the information delivered back to a detector. Here we demonstrate that an electromagnetic wave scattered at an object carries locally defined and conserved information about all of the object’s constitutive parameters. Specifically, we introduce the density and flux of Fisher information for general types of wave fields and identify the corresponding sources and sinks of information through which all these new quantities satisfy a fundamental continuity equation. We experimentally verify our theoretical predictions by studying a movable object embedded in a disordered environment and by measuring the corresponding Fisher information flux at microwave frequencies. Our results improve the understanding of the generation and propagation of information and open up possibilities for tracking and designing the flow of information even in complex environments.

DOI: 10.1038/s41567-024-02519-8

Source: https://www.nature.com/articles/s41567-024-02519-8