Generated Dynamics of Markov and Quantum Processes

Více o knize

This book explores the relationship between Markov and quantum processes as two aspects of generated stochastic processes. It characterizes quantum processes as reversible and generated by one-step unitary operators, while Markov processes are irreversible and generated by one-step stochastic operators. Key features of quantum processes include oscillations, interference, and multiple stationary states in bounded systems, alongside potential asymptotic stationary scattering states in open systems. In contrast, Markov processes exhibit relaxation to a single stationary state. Quantum processes consider all relevant variables affecting reversibility, whereas Markov processes arise when some variables are untraceable, leading to irreversibility. The book aims to show that nearly all theoretical physics subdisciplines can be framed within generated stochastic processes. Deterministic processes in classical mechanics and field theory emerge when fluctuations in relevant variables are minimal, while quantum mechanics deals with genuine quantum processes. It also discusses how relaxing Markov processes can emerge from quantum processes by neglecting numerous uncontrollable variables. Systems with many variables often self-organize, allowing a few slow variables to become relevant. The book emphasizes the importance of symmetries and topological classes in identifying these variables. Additionally, it aims to provide general methods f