论文标题
部分可观测时空混沌系统的无模型预测
Non-Uniform Convergence in Moment Expansions of Integral Work Relations
论文作者
论文摘要
在热力学可观察物的时刻，可以重新铸造积分波动定理中出现的指数平均值。我们使用两个例子表明，这种力矩系列可以在某些单数界限内表现出不均匀的收敛性。第一个示例是一个具有测量和反馈的过程的简单模型。在此示例中，感兴趣的极限是无错误测量值。我们研究的第二个系统是（无限）快速扩张活塞内的理想气体颗粒。两个例子都显示出定性的相似性。低订单的时刻接近其极限价值，而高阶时刻却远离了极限。随着极限的接近，两组矩之间的过渡将推向越来越高的力矩。我们的发现突出了在某些非平衡相关计算中限制限制的重要性。
Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit non-uniform convergence in certain singular limits. The first example is a simple model of a process with measurement and feedback. In this example, the limit of interest is that of error-free measurements. The second system we study is an ideal gas particle inside an (infinitely) fast expanding piston. Both examples show qualitative similarities; the low order moments are close to their limiting value, while high order moments strongly deviate from their limit. As the limit is approached the transition between the two groups of moments is pushed toward higher and higher moments. Our findings highlight the importance of the ordering of limits in certain non-equilibrium related calculations.
