精确可解输运模型中大偏差事件下的电流涨落和统计
Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
摘要：
我们研究的时间积分电流的分布在一个完全可解的玩具模型的热传导，分析和数值。该模型的简单性使我们能够推导出完整的当前大偏差函数和大偏差事件期间的系统统计。通过这种方式，我们揭示了在大偏差事件结束时和中间时间的系统统计之间的关系。中期统计独立于电流的符号，反映了微观动力学的时间反转对称性，而末期统计依赖于电流的符号，也依赖于它的微观定义。我们比较我们的精确结果与模拟的基础上直接评估的大偏差函数，分析这种模拟方法的有限大小的修正，并推导出详细的界限，其适用性。我们还展示了如何Gallavotti-Cohen波动定理可以用来确定模拟结果的有效性范围。
英文摘要：
We study the distribution of the time-integrated current in an exactly-solvable toy model of heat conduction, both analytically and numerically. The simplicity of the model allows us to derive the full current large deviation function and the system statistics during a large deviation event. In this way we unveil a relation between system statistics at the end of a large deviation event and for intermediate times. Midtime statistics is independent of the sign of the current, a reflection of the time-reversal symmetry of microscopic dynamics, while endtime statistics do depend on the current sign, and also on its microscopic definition. We compare our exact results with simulations based on the direct evaluation of large deviation functions, analyzing the finite-size corrections of this simulation method and deriving detailed bounds for its applicability. We also show how the Gallavotti-Cohen fluctuation theorem can be used to determine the range of validity of simulation results.
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