Generated dynamics of Markov and Quantum processes
- 226 pages
- 8 hours of reading
This book explores Markov and quantum processes as two aspects of generated stochastic processes. It examines quantum processes as reversible stochastic processes driven by one-step unitary operators, while Markov processes are characterized as irreversible, generated by one-step stochastic operators. Quantum processes exhibit oscillations, interference, and multiple stationary states in bounded systems, along with potential asymptotic stationary scattering states in open systems. In contrast, Markov processes relax to a single stationary state. Quantum processes consider all relevant variables affecting reversibility, while Markov processes arise when some variables are unobservable and thus irrelevant, leading to irreversibility. The text aims to contextualize various subdisciplines of theoretical physics within generated stochastic processes. Deterministic processes like classical mechanics emerge when fluctuations in relevant variables are minimal, while genuine quantum processes are addressed in quantum mechanics and quantum field theory. The book also discusses how relaxing Markov processes can emerge from quantum processes by omitting numerous uncontrollable variables. Systems with many variables often self-organize, allowing a few slow variables to become relevant. Identifying these variables relies on symmetries and topological classes. Additionally, the book offers general solution methods to find relevant variables