The meromorphic functional calculus developed in Part I overcomes thenondiagonalizability of linear operators that arises often in the temporalevolution of complex systems and is generic to the metadynamics of predictingtheir behavior. Using the resulting spectral decomposition, we deriveclosed-form expressions for correlation functions, finite-length Shannonentropy-rate approximates, asymptotic entropy rate, excess entropy, transientinformation, transient and asymptotic state uncertainty, and synchronizationinformation of stochastic processes generated by finite-state hidden Markovmodels. This introduces analytical tractability to investigating informationprocessing in discrete-event stochastic processes, symbolic dynamics, andchaotic dynamical systems. Comparisons reveal mathematical similarities betweencomplexity measures originally thought to capture distinct informational andcomputational properties. We also introduce a new kind of spectral analysis viacoronal spectrograms and the frequency-dependent spectra of past-future mutualinformation. We analyze a number of examples to illustrate the methods,emphasizing processes with multivariate dependencies beyond pairwisecorrelation. An appendix presents spectral decomposition calculations for oneexample in full detail.
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