Quantum techniques in stochastic mechanics

"We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets -- important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets."--

Intro; Contents; Preface; 1 Stochastic Petri Nets; 1.1. The Rate Equation; 1.2. References; 1.3. Answers; 2 The Rate Equation; 2.1. Rate Equations: The General Recipe; 2.2. The Formation of Water (1); 2.3. The Formation of Water (2); 2.4. The Dissociation of Water (1); 2.5. The Dissociation of Water (2); 2.6. The SI Model; 2.7. The SIR Model; 2.8. The SIRS Model; 2.9. The General Recipe Revisited; 2.10. Answers; 3 The Master Equation; 3.1. The Master Equation; 3.2. Answers; 4 Probabilities vs Amplitudes; 4.1. A Poisson Process; 4.2. Probability Theory vs Quantum Theory.

4.3. Stochastic vs Unitary Operators; 4.4. Infinitesimal Stochastic vs Self-adjoint Operators; 4.5. The Moral; 5 Annihilation and Creation Operators; 5.1. Rabbits and Quantum Mechanics; 5.2. Catching Rabbits; 5.3. Dying Rabbits; 5.4. Breeding Rabbits; 5.5. Dueling Rabbits; 5.6. Brawling Rabbits; 5.7. The General Rule; 5.8. Kissing Rabbits; 5.9. References; 5.10. Answers; 6 An Example from Population Biology; 6.1. Amoeba Fission and Competition; 6.2. The Rate Equation; 6.3. The Master Equation; 6.4. An Equilibrium State; 6.5. Answers; 7 Feynman Diagrams; 7.1. Stochastic Petri Nets Revisited.

7.2. The Rate Equation…