Lanterna Rally

Author: Baez John C

Publisher: World Scientific

Published: 2018-02-14

Total Pages: 276

ISBN-13: 981322696X

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. Keywords: Stochastic;Quantum;Markov Process;Chemical Reaction Network;Petri NetReview: 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