Entropy production and fluctuation theorem along a stochastic limit cycle

Abstract

Entropy production along a trajectory in the stochastic irreversible Brusselator model of chemical oscillating reactions is discussed. Particular attention is paid to a parameter region near the deterministic supercritical Hopf bifurcation. In the stationary state, detailed fluctuation theorem holds due to the reversibility in the state space, which is verified by direct simulations via Gillespie's algorithm [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)]. In addition, we have considered how the entropy production along a noisy limit cycle depends on the system size. Interestingly, in the large system size limit, the entropy production approaches a constant value when the control parameter stays at the deterministic steady state region, while it increases linearly in the deterministic oscillatory region. Such simulation results can be well understood by a stochastic normal form analysis.