Abstract
We introduce dynamics with semi-group or group character. States evolve step by step from an initial state. For reversible systems the group has inverse elements as part of the dynamics. The short time steps are captured by a time homogeneous generator resulting in differential equations in continuous time. States can be configurations, probabilities or pre-probabilities for configurations. We discuss some simple prototypical systems and comment on randomness and determinism in stochastic processes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The difference between semi-group and group is: in semi-groups not every element has an inverse.
- 2.
We use the terms probability density and probability distribution synonymously.
- 3.
The term continuous is used in a broad sense, e.g. \(C^\infty \) if appropriate.
- 4.
So-called fundamental solution or Green’s function of the linear differential equation.
- 5.
Although it was never called that way.
- 6.
This has to be distinguished from a situation where an reversible interacting system is approximated by an effective non-interacting reversible system where each constituent moves in a mean field.
- 7.
Some people like to call it many worlds.
References
D. Dürr, S. Teufel, Bohmian Mechanics—The Physics and Mathematics of Quantum Theory (Springer, Berlin, Heidelberg, 2009)
A.S.Sanz, S.Miret-Artes, A Trajectory Description of Quantum Processes. Vol. I Fundamentals and Vol. II Applications (Springer 2012 and 2014)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Janßen, M. (2016). Generated Dynamics. In: Generated Dynamics of Markov and Quantum Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49696-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-49696-1_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-49694-7
Online ISBN: 978-3-662-49696-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)