You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Entropy Applications to Water Monitoring Network Design: A Review 
Chapter Title:  Total Correlation 
1. Abstract of Cited Paper (BIB001):  A set λ of stochastic variables, y1, y2,..., yn, is grouped into subsets, µ1, µ2,..., µk. The correlation existing in λ with respect to the µ's is adequately expressed by C= Σi=1k S(µi)-S(λ)≥0, where S(v) is the entropy function defined with reference to the variables y in subset v. For a given λ, C becomes maximum when each µi consists of only one variable, (n=k). The value Cis then called fhe total correlation in λ, Ctot(λ). The present paper gives various theorems, according to which Ctot(λ) can be decomposed in terms of the partial correlations existing in subsets of λ, and of quantities derivable therefrom. The information-theoretical meaning of each decomposition is carefully explained. As illustrations, two problems are discussed at the end of the paper: (1) redundancy in geometrical figures in pattern recognition, and (2) randomization effect of shuffling cards marked "zero' or "one."

Literature Review:
While transinformation and mutual information have the same definition, total correlation is not equivalent to them as the total correlation is a simple estimate that defines the amount of shared information typically of multiple variables. Simply, the total correlation is defined by the difference between the sum of marginal entropy of N variables and their joint entropy BIB001 BIB002 , which is given as: If N = 2 in Equation (14), the total correlation will be equal to the transinformation or mutual information. However, the transinformation is only meaningful to two random variables as shown in Equations (11) to (13); therefore, the total correlation and the transinformation values would be different if N > 2.