Network Theory

John Baez

March 23, 2013

Parts 2 to 24 are being made into a book:

• John Baez and Jacob Biamonte, A Course on Quantum Techniques for Stochastic Mechanics.

• John Baez and Brendan Fong, A Noether theorem for stochastic mechanics, to appear in Jour. Math. Phys..
• John Baez, Quantum techniques for reaction networks.
• John Baez and Brendan Fong, Quantum techniques for studying equilibrium in reaction networks.

The blog articles

• Part 1 - toward a general theory of networks. Also available on Azimuth.
• Part 2 - stochastic Petri nets; the master equation versus the rate equation. Also available on Azimuth.
• Part 3 - the rate equation of a stochastic Petri net, and applications to chemistry and infectious disease. Also available on Azimuth.
• Part 4 - the master equation of a stochastic Petri net, and analogies to quantum field theory. Also available on Azimuth.
• Part 5 - the stochastic Petri net for a Poisson process; analogies between quantum theory and probability theory. Also available on Azimuth.
• Part 6 - the master equation in terms of annihilation and creation operators. Also available on Azimuth.
• Part 7 - a stochastic Petri net from population biology whose rate equation is the logistic equation; an equilibrium solution of the corresponding master equation. Also available on Azimuth.
• Part 8 - the rate equation and master equation of a stochastic Petri net; the role of Feynman diagrams. Also available on Azimuth.
• Part 9 - the Anderson–Craciun–Kurtz theorem, which gives equilibrium solutions of the master equation from complex balanced equilibrium solutions of the rate equation; coherent states. Also available on Azimuth.
• Part 10 - an example of the Anderson-Craciun-Kurtz theorem. Also available on Azimuth.
• Part 11 - a stochastic version of Noether's theorem. Also available on Azimuth.
• Part 12 - comparing quantum mechanics and stochastic mechanics. Also available on Azimuth.
• Part 13 - comparing the quantum and stochastic versions of Noether's theorem. Also available on Azimuth.
• Part 14 - an example: chemistry and the Desargues graph. Also available on Azimuth, together with a special post on answers to the puzzle.
• Part 15 - Markov processes and quantum processes coming from graph Laplacians, illustrated using the Desargues graph. Also available on Azimuth.
• Part 16 - Dirichlet operators and electrical circuits made of resistors. Also available on Azimuth.
• Part 17 - reaction networks versus Petri nets; the deficiency zero theorem. Also available on Azimuth.
• Part 18 - an example of the deficiency zero theorem: a diatomic gas. Also available on Azimuth
• Part 19 - an example of Noether's theorem and the Anderson–Craciun–Kurtz theorem: a diatomic gas. Also available on Azimuth.
• Part 20 - Dirichlet operators and the Perron–Frobenius theorem. Also available on Azimuth.
• Part 21 - warmup for the proof of the deficiency zero theorem: the concept of deficiency. Also available on Azimuth.
• Part 22 - warmup for the proof of the deficiency zero theorem: reformulating the rate equation. Also available on Azimuth.
• Part 23 - warmup for the proof of the deficiency zero theorem: finding the equilibria of a Markov process, and describing its Hamiltonian in a slick way. Also available on Azimuth.
• Part 24 - proof of the deficiency zero theorem. Also available on Azimuth.
• Part 25 - Petri nets, logic, and computation: the reachability problem for Petri nets. Also available on Azimuth.

© 2012 John Baez
baez@math.removethis.ucr.andthis.edu

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