Some new insights on informational entropy for water distribution networks

Several researchers have studied the use of informational entropy as a surrogate measure for the reliability of water distribution networks. The hypothesis is that the numerical value of network entropy in some way reflects the reliability of water distribution networks, and this appears to be supported by the analysis of some example water distribution networks. However, the precise relationship between the entropy value and some measures of reliability has not been formally established. The primary objective in this paper is to present an alternative methodology to calculate the informational entropy of water distribution networks. This methodology is termed as the Path Entropy Method (PEM), which provides some insights into the entropy of branching-tree networks and maximum-entropy flows of single-source networks. In addition, a quick method of computing the maximum-entropy value of single-source networks is presented and termed as the Simplified Path Entropy Method (SPEM).