> For the complete documentation index, see [llms.txt](https://v2tech.noahlabs.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://v2tech.noahlabs.io/2.mathematical-derivation-of-hmm-model-and-quantum-entropy-reduction.md).

# 2.Mathematical Derivation of HMM Model and Quantum Entropy Reduction

- [2.1 HMM Protocol: Liquidity is Permanent Infrastructure](https://v2tech.noahlabs.io/2.mathematical-derivation-of-hmm-model-and-quantum-entropy-reduction/2.1-hmm-protocol-liquidity-is-permanent-infrastructure.md)
- [2.2 Black Hole Mechanism and the Thermodynamic Death of LP Tokens](https://v2tech.noahlabs.io/2.mathematical-derivation-of-hmm-model-and-quantum-entropy-reduction/2.2-black-hole-mechanism-and-the-thermodynamic-death-of-lp-tokens.md)
- [2.3 Reverse Execution and System Stability of Automated Market Maker](https://v2tech.noahlabs.io/2.mathematical-derivation-of-hmm-model-and-quantum-entropy-reduction/2.3-reverse-execution-and-system-stability-of-automated-market-maker.md)