Theorem of inevitable death: dissipative cycle, reinvestment and survival criterion for complex systems

This paper establishes a mathematical isomorphism between a stick-slip oscillator and a class of dissipative systems with reinvestment. We derive equations for resource (m), variability (g), and consolidation (k) dynamics. Key results include: the theorem of inevitable death under fixed strategies, survival criterion requiring negative feedback, irreversibility threshold for system ensembles, necessity of phase transitions between fermionic and bosonic regimes, and cascading evolutionary explosions with exponential acceleration. A quantum of metabolic power P is introduced. Spectral power density is shown to be mathematically isomorphic to Planck's formula, revealing deep connections between dissipative systems and quantum statistics.