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Discreteness-induced transitions in multibody reaction systems
Yohei Saito1, Yuki Sughiyama1,2, Kunihiko Kaneko2
1Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505 Japan.
Physical Review. E
|September 15, 2016
Summary
Small systems can behave differently than large ones due to discreteness. This study introduces a minimal model to understand discreteness-induced transitions in reaction systems.
Area of Science:
- Chemical kinetics
- Nonlinear dynamics
- Systems biology
Background:
- Macroscopic systems exhibit predictable behavior.
- Small systems can display unique dynamics, termed small-size transitions.
- These transitions are often attributed to increased noise or state space discreteness.
Purpose of the Study:
- To investigate the under-analyzed discreteness-induced mechanism of small-size transitions.
- To propose a minimal model capturing the essence of discreteness effects.
- To identify conditions for discreteness-induced transitions in complex systems.
Main Methods:
- Development of a one- and three-body reaction system as a minimal model.
- Analysis of the discreteness-induced transition mechanism.
- Derivation of conditions for transition occurrence in broader systems.
Main Results:
- A minimal model for discreteness-induced transitions was successfully proposed.
- The study clarifies the distinction between noise and discreteness effects.
- Conditions governing these transitions were derived.
Conclusions:
- The proposed model offers a new perspective on small-size transitions.
- Understanding discreteness is crucial for modeling small systems.
- This research advances the comprehension of system size effects on behavior.
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