Σ̇ Market Intelligence¶
Live Tool: → Open the Entropy Regime Detector
What It Does¶
Applies the RTSG Ginzburg-Landau framework to financial markets in real-time. Enter any ticker symbol and get:
- Entropy Σ — Shannon entropy of rolling return distribution (structural diversity)
- Entropy Rate Σ̇ — Rate of change of Σ (structural production speed)
- Correlation Length ξ_W — Autocorrelation decay (how far price moves propagate)
- Lyapunov λ — Stability exponent (ordered/critical/disordered classification)
- Mass Gap Δ — Minimum entropy cost of regime excitation (1/ξ_W)
- Σ̇ Divergence — Is entropy production accelerating without structural coherence?
- GL Regime — Ordered / Critical / Disordered phase classification
- Signal — Hold / Opportunity / Caution / Danger
The Key Signal: Σ̇ Divergence Without ξ_W Increase¶
The primary danger signal is:
Σ̇ accelerating (entropy production speeding up) while ξ_W stays flat or drops (structural coherence not increasing)
This means the market is producing entropy (disorder) faster but not building new structure. It is the GL signature of approaching dissolution — a crash or regime breakdown.
Conversely, Σ̇ rising WITH ξ_W rising means the market is at a productive critical point — a potential opportunity.
GL Regime Classification¶
| Regime | λ | Σ̇ | ξ_W | Market State | Action |
|---|---|---|---|---|---|
| Ordered | < 0 | Low, steady | Long | Trending. Condensed phase. | Hold trend |
| Critical | ≈ 0 | High | Diverging | Phase boundary. Maximum information. | Opportunity or danger — check Σ̇/ξ_W ratio |
| Disordered | > 0 | Spiking then crashing | Short | Dissolution. Structure breaking down. | Reduce exposure |
Mathematical Foundation¶
The tool implements the entropy framework from:
- Action-Entropy Identity: \(S_E = -\Sigma\)
- GL Theory — Entropy Dual: phase transitions as entropy regimes
- Σ-Reparameterization: \(d/dt \to \dot\Sigma\,d/d\Sigma\)
- Master Reference v4: updated equation set
The mass gap \(\Delta = \sqrt{2\alpha} = 1/\xi_W\) is the minimum entropy cost of disrupting the current regime. When \(\Delta \to 0\), regime change is free — phase transition imminent.
Disclaimer¶
This tool is for educational and research purposes only. It is not financial advice. Past entropy patterns do not guarantee future market behavior. The RTSG framework is a research program, not a proven trading system. Use at your own risk.