Fluctuation Statistics

Fluctuation Statistics are the statistical description of the substrate at equilibrium before ignition: energy fluctuations with zero mean and a variance equal to the Fluctuation Amplitude. They characterize the Equilibrium Conditions in which random fluctuations hang between dissipation and ignition. From this background, isolated energy concentrations form with probability exp(−E⨶/(k_B T▱)), but remain transient because they lack the recursive feedback needed for self-amplification; only accumulations meeting the Recursive Stability Criterion become stable loops that fuel recursive processing. ⟨E⌇⟩ = 0 and Var(E⌇) = σ²▱, where E⌇ is the substrate energy fluctuation, tagged [J], and σ²▱ is the Fluctuation Amplitude, tagged [J²]. They characterize Equilibrium Conditions through the Fluctuation Amplitude, and connect to Proto-Nova Formation Probability, Isolated Energy Concentrations and Recursive Stability Criterion.