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The signature matrix of an n-component three-state network (system), which depends only on the network structure, is a useful tool for comparing the reliability and stochastic properties
of networks. In this paper, we consider a three-state network with states up, partial performance, and down. We assume that the network remains in state up, for a random time T 1 and then moves to state partial performance until it fails at time T > T 1 . The signature-based expressions for the conditional entropy of T given T 1 , the joint entropy, Kullback-Leibler (K-L)
information, and mutual information of the lifetimes T and T 1 are presented. It is shown that the K-L information, and mutual information between T 1 and T depend only on the network structure (i.e., depend only to the signature matrix of the network). Some signature-based
stochastic comparisons are also made to compare the K-L of the state lifetimes in two different three-state networks. Upper and lower bounds for the K-L divergence and mutual information between T 1 and T are investigated. Finally the results are extended to n-component multi-state networks. Several examples are examined graphically and numerically.
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