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A mathematical isomorphism between a stick-slip oscillator and a class of dissipative systems with reinvestment is established. Equations for the dynamics of resource, variability, and consolidation are derived. The theorem of inevitable demise under fixed strategies, the survival criterion through negative feedback, the irreversibility threshold for ensembles of systems, the necessity of phase switching between fermionic and bosonic regimes, and a cascade of evolutionary explosions with exponential acceleration are proven. A quantum of metabolic power is introduced. It is shown that the spectral power density is mathematically isomorphic to Planck's formula, revealing deep connections between dissipative systems and quantum statistics. The theory is illustrated with examples from DNA biophysics, the evolution of large language models (LLMs), economics (Pareto distribution), and social systems (Zipf's law). Worldview implications are discussed.
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