An Entropy Based Measure for Comparing Distributions of Complexity
Physica A: Statistical Mechanics and Its Applications
Probability distributions, Complex systems, Shannon entropy, Measures of complexity
Mathematics | Physical Sciences and Mathematics | Social Statistics | Sociology | Statistics and Probability
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 pi , 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 Cc — a modification of the Shannon–Wiener entropy measure H. The utility of this measure is that, unlike current complexity measures–which focus on the macroscopic complexity of a single system–Cc can be used to empirically identify and measure the 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.
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