AI summary · arXiv: 1409.1439v1 · cond-mat.stat-mech
System size expansion using Feynman rules and diagrams
The essentials
- The authors address the challenge of studying large fluctuations in stochastic systems
- They develop a simple diagrammatic approach to the Chemical Master Equation
- The approach allows for the calculation of multi-time correlation functions with high accuracy using van Kampen's system size expansion
- The authors present a set of Feynman rules for constructing a diagrammatic perturbation expansion algorithmically
- These rules enable calculations up to any desired order in the system size expansion, providing a powerful tool for quantitative studies of stochastic systems
- The methodology is applied to biochemical reaction networks and closed-form expressions for leading order corrections to the linear noise approximation are derived
- The corrections reveal noise-induced oscillations in the Brusselator reaction scheme that are not captured by commonly used approximations like the linear noise approximation
- The diagrammatic approach offers insights into complex dynamics and fluctuations in stochastic systems that would otherwise be missed
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