Seitz W, Kirwan A D
Department of Marine Sciences, Texas A&M University at Galveston, Galveston, TX 77553, USA.
School of Marine Science and Policy, University of Delaware, Newark, DE 19716, USA.
Entropy (Basel). 2022 Aug 8;24(8):1090. doi: 10.3390/e24081090.
can be traced to unpublished notes by Josiah Gibbs. Subsequently, the concept was developed independently, and under somewhat different names, by other investigators. The central idea of mixed-up-ness is that systems states can be organized in a hierarchy by their degree of mixed-up-ness. In its purest form, the organizing principle is independent of thermodynamic and statistical mechanics principles, nor does it imply irreversibility. Yet, Gibbs and subsequent investigators kept entropy as the essential concept in determining system evolution, thus retaining the notion that systems evolve from states of perfect "order" to states of total "disorder". Nevertheless, increasing mixed-up-ness is consistent with increasing entropy; however, there is no unique one-to-one connection between the two. We illustrate the notion of mixed-up-ness with an application to the permutation function of integer partitions and then formalize the notion of mixed-up-ness as a fundamental hierarchal principle, the law of mixed-up-ness (LOM), for non-thermodynamic systems.
可以追溯到约西亚·吉布斯未发表的笔记。随后，其他研究者独立地发展了这一概念，且名称略有不同。“混乱度”的核心思想是，系统状态可以根据其混乱程度组织成一个层次结构。在其最纯粹的形式中，组织原则独立于热力学和统计力学原则，也不意味着不可逆性。然而，吉布斯及后续研究者在确定系统演化时将熵作为核心概念，从而保留了系统从完美“有序”状态演变为完全“无序”状态的观念。尽管如此，增加的混乱度与增加的熵是一致的；然而，两者之间并没有唯一的一一对应关系。我们通过将其应用于整数划分的置换函数来说明混乱度的概念，然后将混乱度的概念形式化为非热力学系统的一个基本层次原则，即混乱度定律（LOM）。
