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Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time averaged entropy productionP on the system sizeN in a parameter region close to the deterministic Hopf bifurcation.In the large system size (weak noise) limit, we find that P N^β with β=0 or 1 when the system is below or abovethe Hopf bifurcation, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly,P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears.This phenomenon could be qualitativelyunderstood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.