Excerpt

Rudolf Clausius described entropy for thermodynamics in 1865, and Ludwig Boltzmann, Josiah Willard Gibbs, James Clerk Maxwell, and others expanded the concept into statistical mechanics. Claude Elwood Shannon also introduced a new aspect of entropy into information theory during 1948.1 Consequently, the long, notable history of entropy studies has facilitated understanding of the laws of nature. Among several equations for entropy that are applied across many scientific disciplines, the Shannon equation (\( H = - \sum p_{i} \log p_{i} \), where p_i is the probability of state i) that is based on information theory is applied to phase analyses of gated single-photon emission computed tomography (SPECT). In phase histograms generated from gated SPECT data, p_i represents the frequency of the histogram bin i. Entropy increases if the phase distribution becomes disordered in histograms. If the equation for entropy is divided by log (n), in which n represents the number of histogram bins, the entropy range is 0-1, which represents total order to disorder. …