Shannon entropy of the return distribution over a rolling window. Measures the diversity of market states — how many distinguishable configurations the market has visited recently. Higher Σ = more disorder, more information.
Rate of change of Σ. When Σ̇ accelerates without corresponding increase in ξ_W, the market is approaching dissolution — entropy production is outrunning structural coherence. This is the primary sell signal.
Autocorrelation decay length of returns. Measures how far price movements propagate in time. Long ξ = trending (ordered). Short ξ = random walk (disordered). Diverging ξ = phase transition (critical).
Ordered (λ < 0): Trending market. Condensed phase. Safe to hold trend. Critical (λ ≈ 0): Phase boundary. Maximum information. Opportunity or danger. Disordered (λ > 0): Dissolution. Structure breaking down. Reduce exposure.
Minimum entropy cost of a regime excitation: Δ = √(2α) = 1/ξ_W. Large gap = stable regime, expensive to disrupt. Small gap = fragile regime, cheap to break. Gap approaching zero = phase transition imminent.
Hold: Ordered regime, stable Σ̇. Opportunity: Critical regime, Σ̇ rising with ξ_W. Caution: Σ̇ accelerating, ξ_W stable. Danger: Σ̇ diverging, ξ_W collapsing. The key: Σ̇ divergence WITHOUT ξ_W increase = sell.