Compression-Resonance Thermodynamic Index (CRTI): A Theoretical Framework for Detecting Systemic Instability

Many complex systems collapse not due to randomness but due to structural over-compression and loss of adaptive capacity. This paper introduces the Compression–Resonance Thermodynamic Index (CRTI) — a structural diagnostic framework for detecting systemic instability in complex adaptive systems. CRTI is defined as CRTI(t) = C(t) · ln(1 + R(t)), where C(t) denotes structural compression and R(t) denotes systemic resonance capacity.The framework identifies a resonance corridor within which systems remain adaptive, and characterizes departures from this corridor as structural precursors to catastrophic regime shifts. A minimal dynamical model is presented, demonstrating bifurcation behaviour driven by rising compression and declining resonance. CRTI is positioned against established frameworks including the Scheffer–Dakos early-warning signal theory, Holling’s adaptive cycle, the May–Wigner stability criterion, and network percolation models. Potential empirical applications are discussed for ecological systems, financial networks, organizations, and socio-technical platforms.Keywords: complex adaptive systems · structural instability · early-warning signals · resonance capacity · compression dynamics · regime shifts · bifurcation · systemic risk · complexity science · systems theory · CRTI · Mallinckrodt Framework