Abstract
We review recent developments in the conceptual approach to a consistent systematic understanding of cooperative thermodynamic activity. The microcanonical statistical analysis is a powerful tool that is particularly useful for the investigation of analogs of phase transitions in finite systems, but it applies also in the extrapolation toward the thermodynamic limit. Whereas Maxwell construction in the coexistence region in the inverse caloric temperature space is a reasonable method for individual first-order-like transitions that are well-separated from other energetic regions of thermal activity, microcanonical inflection-point analysis is a systematic method that enables both the identification and classification of transitions of first and higher orders.
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