具有振荡和可激发动力学的介观化学反应系统的熵产生
Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics
摘要：
化学反应系统的随机热力学近年来受到广泛关注。在本文中，我们以铂晶体表面一氧化碳的催化氧化为例，考虑了具有振荡动力学和可激发动力学的系统的这样一个问题。从化学朗之万方程出发，我们能够计算浓度状态空间中沿随机轨迹的随机熵产生P。在接近确定性Hopf分支的参数区域内，研究了时间平均熵产生P对系统尺寸N的依赖关系，在大系统尺寸（弱噪声）极限下，发现系统在Hopf分支以下或以上时，P N^β分别满足β=0或1.在小系统尺寸（强噪声）限制下，P总是随N线性增加，而与分叉参数无关。更有趣的是，P甚至可以达到一个最大值的一些中间系统的大小在一个参数区域中，相应的确定性系统显示出稳态或小振幅振荡。P的最大值随着系统参数接近最大值消失的CANARD点而减小，这一现象可以通过将总熵产生分为尖峰和小振幅振荡的贡献来定性地理解。
英文摘要：
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.
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