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Entropy production and fluctuation theorem along a stochastic limit cycle
Tie Jun Xiao1, Zhonghuai Hou, Houwen Xin
1Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
The Journal of Chemical Physics
|December 3, 2008
Summary
This study explores entropy production in the Brusselator model, revealing how it behaves near bifurcations. Near the Hopf bifurcation, entropy production stabilizes in large systems at steady states but grows in oscillatory regions.
Area of Science:
- Chemical kinetics
- Non-equilibrium thermodynamics
- Stochastic processes
Background:
- The Brusselator model is a key system for studying chemical oscillations.
- Understanding entropy production is crucial for irreversible processes.
- Near bifurcations, stochastic effects become significant in chemical reactions.
Purpose of the Study:
- To investigate entropy production in the stochastic Brusselator model near a supercritical Hopf bifurcation.
- To analyze the dependence of entropy production on system size along noisy limit cycles.
- To verify theoretical predictions with numerical simulations.
Main Methods:
- Stochastic simulation using Gillespie's algorithm.
- Analysis of entropy production along trajectories.
- Stochastic normal form analysis.
- Investigation of the parameter region near the deterministic supercritical Hopf bifurcation.
Main Results:
- Detailed fluctuation theorem holds in the stationary state due to state space reversibility.
- Entropy production approaches a constant value in the large system size limit for steady states.
- Entropy production increases linearly with system size in the deterministic oscillatory region.
- Simulation results align with stochastic normal form analysis.
Conclusions:
- The study provides insights into entropy production dynamics in a key model of chemical oscillations.
- System size significantly influences entropy production near bifurcations.
- Stochastic normal form analysis effectively explains the observed simulation results.
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