Entropy
Entropy
复制标题
DOI：
10.7551/mitpress/11924.003.0011
复制
发表时间：
2022-01
期刊：
影响因子：
--
通讯作者：
C. Tsallis
中科院分区：
文献类型：
--
作者：
C. Tsallis
熵的概念与能量一起构成了当代物理学和相关领域的基石。它最初是由克劳修斯在1865年沿着抽象的路线介绍的，重点是宏观物理过程的物理不可逆性。在接下来的十年里，玻尔兹曼将熵与微观世界天才地联系起来，吉布斯进一步发展了这一联系，这导致了一个新的、令人印象深刻的成功的物理理论的形成，此后被命名为统计力学。冯·诺依曼在1927年将量子力学系统的扩展形式化，香农在1948年和杰恩斯在1957年分别介绍了与通信理论和更广泛的信息理论的联系。从那时起，超过50个新的熵泛函出现在科技文献中。其中最受欢迎的是1961年引入的Renyi加法和1988年引入的非加法，作为Boltzmann-Gibbs和相关平衡和非平衡理论的推广基础，专注于自然，人工和社会复杂系统。沿着这样的路线，理论、实验、观测和计算的努力，以及它们与非线性动力系统和概率论的联系，目前正在取得进展。在本概要中简要介绍了这些最新发展在物理学和其他方面的说明性应用。
The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas. It was originally introduced by Clausius in 1865 along abstract lines focusing on thermodynamical irreversibility of macroscopic physical processes. In the next decade, Boltzmann made the genius connection—further developed by Gibbs—of the entropy with the microscopic world, which led to the formulation of a new and impressively successful physical theory, thereafter named statistical mechanics. The extension to quantum mechanical systems was formalized by von Neumann in 1927, and the connections with the theory of communications and, more widely, with the theory of information were respectively introduced by Shannon in 1948 and Jaynes in 1957. Since then, over fifty new entropic functionals emerged in the scientific and technological literature. The most popular among them are the additive Renyi one introduced in 1961, and the nonadditive one introduced in 1988 as a basis for the generalization of the Boltzmann–Gibbs and related equilibrium and nonequilibrium theories, focusing on natural, artificial and social complex systems. Along such lines, theoretical, experimental, observational and computational efforts, and their connections to nonlinear dynamical systems and the theory of probabilities, are currently under progress. Illustrative applications, in physics and elsewhere, of these recent developments are briefly described in the present synopsis.