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.
Contents: Stochastic Petri NetsThe Rate EquationThe Master EquationProbabilities vs AmplitudesAnnihilation and Creation OperatorsAn Example from Population BiologyFeynman DiagramsThe Anderson–Craciun–Kurtz TheoremAn Example of the Anderson–Craciun–Kurtz TheoremA Stochastic Version of Noether's TheoremQuantum Mechanics vs Stochastic MechanicsNoether's Theorem: Quantum vs StochasticChemistry and the Desargues GraphGraph LaplaciansDirichlet Operators and Electrical CircuitsPerron–Frobenius TheoryThe Deficiency Zero TheoremExample of the Deficiency Zero TheoremExample of the Anderson–Craciun–Kurtz TheoremThe Deficiency of a Reaction NetworkRewriting the Rate EquationThe Rate Equation and Markov ProcessesProof of the Deficiency Zero TheoremNoether's Theorem for Dirichlet OperatorsComputation and Petri NetsSummary 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 theoryIt explains how stochastic Petri nets can be used in modeling in biology, chemistry, and many other fieldsIt gives new proofs of some fundamental theorems about chemical reaction networks