具有隐藏慢自由度网络中表观熵产生的涨落
Fluctuations of Apparent Entropy Production in Networks with Hidden Slow Degrees of Freedom
摘要：
熵产生的涨落定理是一个显着的对称性的产生的熵的分布，普遍适用于非平衡定态马尔可夫动力学。然而，在观察者看不到的慢自由度系统中，不可能准确地推断出产生的熵的量。以前的工作表明，类似于涨落定理的关系可能至少近似地适用于这样的系统，如果考虑表观熵产生的话。通过将表观熵产生的概念扩展到离散二分系统，我们研究了这种修改后的波动定理在大偏差极限下必须满足哪些标准。我们使用的大偏差函数的渐近近似表明，表观熵产生的极端事件的概率总是服从修改后的波动定理，而且，它是可能的，以推断其他隐藏的属性。对于环上两个耦合胶体粒子的典型情况，计算表观熵产生的速率函数，以说明这种渐近行为，并表明在短观测时间内实验观察到的修改后的波动定理在长时间限制下不存在。
英文摘要：
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of freedom that are hidden from the observer, it is not possible to infer the amount of produced entropy exactly. Previous work suggested that a relation similar to the fluctuation theorem may hold at least approximately for such systems if one considers an apparent entropy production. By extending the notion of apparent entropy production to discrete bipartite systems, we investigate which criteria have to be met for such a modified fluctuation theorem to hold in the large deviation limit. We use asymptotic approximations of the large deviation function to show that the probabilities of extreme events of apparent entropy production always obey a modified fluctuation theorem and, moreover, that it is possible to infer otherwise hidden properties. For the paradigmatic case of two coupled colloidal particles on rings the rate function of the apparent entropy production is calculated to illustrate this asymptotic behavior and to show that the modified fluctuation theorem observed experimentally for short observation times does not persist in the long time limit.
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