#### Title

An Entropy Based Measure for Comparing Distributions of Complexity

#### Publication Title

Physica A: Statistical Mechanics and Its Applications

#### Publication Date

7-2016

#### Document Type

Article

#### DOI

10.1016/J.PHYSA.2016.02.007

#### Keywords

Probability distributions, Complex systems, Shannon entropy, Measures of complexity

#### Disciplines

Mathematics | Physical Sciences and Mathematics | Social Statistics | Sociology | Statistics and Probability

#### Abstract

This paper is part of a series addressing the empirical/statistical distribution of the diversity of complexity within and amongst complex systems. Here, we consider the problem of measuring the diversity of complexity in a system, given its ordered range of complexity types *i* and their probability of occurrence *p _{i }*, with the understanding that larger values of

*i*mean a higher degree of complexity. To address this problem, we introduce a new complexity measure called

*case-based entropy C*— a modification of the Shannon–Wiener entropy measure

_{c}*H*. The utility of this measure is that, unlike current complexity measures–which focus on the macroscopic complexity of a single system–

*C*can be used to empirically identify and measure the

_{c}*distribution of the diversity of complexity*within and across multiple natural and human-made systems, as well as the diversity contribution of complexity of any part of a system, relative to the total range of ordered complexity types.

#### Recommended Citation

Rajaram, Rajeev and Castellani, Brian (2016). An Entropy Based Measure for Comparing Distributions of Complexity. *Physica A: Statistical Mechanics and Its Applications* 453(1), 35-43. doi: 10.1016/J.PHYSA.2016.02.007 Retrieved from https://digitalcommons.kent.edu/socpubs/37

#### Publisher

Elsevier

#### Publisher Location

Amsterdam, Netherlands