Our book is now available through World Scientific Publishing. A preprint of the book remains open access on the arXiv and here. The book was published as
Quantum Techniques in Stochastic Mechanics
John C. Baez and Jacob D. Biamonte
World Scientific Publishing, 276 pages (2018)
[link to get the book from WS]
The book constructs a detailed analogy between quantum mechanics and the theory of random processes. We called the latter stochastic mechanics.
The book should be of interest to graduate students and advanced undergraduates who are leaning quantum theory. It should also be of interest to reachers working in statistical physics and complex network theory who are interested in using quantum inspired methods in their work. Finally, I personally believe that the text should be of interest to quantum physics researchers interested in the foundations of physics.
You can read all about it online free and decide if you want an actual hardcopy. The arXiv abstract reads
Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of “chemical reaction networks”, which describes the interactions of molecules in a stochastic rather than quantum way. Computer science and population biology use the same ideas under a different name: “stochastic Petri nets”. But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas – but in a context where probabilities replace amplitudes. We explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics. We use this analogy to present new proofs of two major results in the theory of chemical reaction networks: the deficiency zero theorem and the Anderson-Craciun-Kurtz theorem. We also study the overlap of quantum mechanics and stochastic mechanics, which involves Hamiltonians that can generate either unitary or stochastic time evolution. These Hamiltonians are called “Dirichlet forms”, and they arise naturally from electrical circuits made only of resistors.
