Quantum Techniques in Stochastic Mechanics
Nonfiction, Science & Nature, Mathematics, Probability, Science, Physics, Quantum Theory, Statistics
| Author: | John Baez, Jacob D Biamonte | ISBN: | 9789813226968 |
| Publisher: | World Scientific Publishing Company | Publication: | February 14, 2018 |
| Imprint: | WSPC | Language: | English |
| Author: | John Baez, Jacob D Biamonte |
| ISBN: | 9789813226968 |
| Publisher: | World Scientific Publishing Company |
| Publication: | February 14, 2018 |
| Imprint: | WSPC |
| Language: | English |
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.
Contents:
- Stochastic Petri Nets
- The Rate Equation
- The Master Equation
- Probabilities vs Amplitudes
- Annihilation and Creation Operators
- An Example from Population Biology
- Feynman Diagrams
- The Anderson–Craciun–Kurtz Theorem
- An Example of the Anderson–Craciun–Kurtz Theorem
- A Stochastic Version of Noether's Theorem
- Quantum Mechanics vs Stochastic Mechanics
- Noether's Theorem: Quantum vs Stochastic
- Chemistry and the Desargues Graph
- Graph Laplacians
- Dirichlet Operators and Electrical Circuits
- Perron–Frobenius Theory
- The Deficiency Zero Theorem
- Example of the Deficiency Zero Theorem
- Example of the Anderson–Craciun–Kurtz Theorem
- The Deficiency of a Reaction Network
- Rewriting the Rate Equation
- The Rate Equation and Markov Processes
- Proof of the Deficiency Zero Theorem
- Noether's Theorem for Dirichlet Operators
- Computation and Petri Nets
- Summary Table
Readership: Graduate students and researchers in the field of quantum and mathematical physics.
Key Features:
- It's a light-hearted introduction to a deep analogy between probability theory and quantum theory
- It explains how stochastic Petri nets can be used in modeling in biology, chemistry, and many other fields
- It gives new proofs of some fundamental theorems about chemical reaction networks
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.
Contents:
- Stochastic Petri Nets
- The Rate Equation
- The Master Equation
- Probabilities vs Amplitudes
- Annihilation and Creation Operators
- An Example from Population Biology
- Feynman Diagrams
- The Anderson–Craciun–Kurtz Theorem
- An Example of the Anderson–Craciun–Kurtz Theorem
- A Stochastic Version of Noether's Theorem
- Quantum Mechanics vs Stochastic Mechanics
- Noether's Theorem: Quantum vs Stochastic
- Chemistry and the Desargues Graph
- Graph Laplacians
- Dirichlet Operators and Electrical Circuits
- Perron–Frobenius Theory
- The Deficiency Zero Theorem
- Example of the Deficiency Zero Theorem
- Example of the Anderson–Craciun–Kurtz Theorem
- The Deficiency of a Reaction Network
- Rewriting the Rate Equation
- The Rate Equation and Markov Processes
- Proof of the Deficiency Zero Theorem
- Noether's Theorem for Dirichlet Operators
- Computation and Petri Nets
- Summary Table
Readership: Graduate students and researchers in the field of quantum and mathematical physics.
Key Features:
- It's a light-hearted introduction to a deep analogy between probability theory and quantum theory
- It explains how stochastic Petri nets can be used in modeling in biology, chemistry, and many other fields
- It gives new proofs of some fundamental theorems about chemical reaction networks
