Event-scale analysis techniques using correlation and fluctuation measures are applied to heavy-ion collision data with the goal of discovering, characterizing, and understanding deconfined quark matter. In service of these goals development of a scale-local thermodynamics is discussed and applied to a broad range of toy models, simulations, and data. Scale-local partitioning is discussed at length and an ideal theoretical reference is derived for comparison to data. The dimension of the chaotic attractor of the Hénon map is calculated as a function of scale, and the implications of scale-local dimension are explored. Event spaces with discriminatory power are developed and applied to the face recognition problem, detector triggering, and STAR and NA49 data. Event-wise mean transverse momentum fluctuations in STAR data are analyzed with a minimally biased central-limit based measure using numerical and graphical methods. Cut efficiencies, corrections, and systematic error sources are all addressed. A connection between non-statistical fluctuations and two-particle correlations is found and exploited. Two-particle correlation space formation is discussed and methods for minimizing error from event mixing are discovered. Central data from STAR and NA49 are analyzed, confirming the results of the fluctuation analysis and providing additional insight into the physics sources contributing to correlations in heavy-ion collisions.
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