We present experimental evidence that, together with the integral fluctuation theorem, which is fulfilled with high accuracy, a detailed-like fluctuation theorem holds for large entropy values in cascade processes in turbulent flows. Based on experimental data, we estimate the stochastic equations describing the scale-dependent cascade process in a turbulent flow by means of Fokker-Planck equations, and from the corresponding individual cascade trajectories an entropy term can be determined. Since the statistical fluctuation theorems set the occurrence of positive and negative entropy events in strict relation, we are able to verify how cascade trajectories, defined by entropy consumption or entropy production, are linked to turbulent structures: Trajectories with entropy production start from large velocity increments at large scale and converge to zero velocity increments at small scales; trajectories with entropy consumption end at small scale velocity increments with finite size and show a lower bound for small scale increments. A linear increase with the magnitude of the negative entropy value is found. This indicates a tendency to local discontinuities in the velocity field. Our findings show no lower bound of negative entropy values and thus for the corresponding piling up velocity differences of the small scale structures.

中文翻译：

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从熵和涨落定理看湍流的小尺度结构

我们提供的实验证据表明，与高精度实现的积分涨落定理一起，湍流中级联过程中的大熵值适用于详细的涨落定理。基于实验数据，我们利用Fokker-Planck方程估计描述湍流中与尺度相关的级联过程的随机方程，并且可以从相应的单个级联轨迹确定熵项。由于统计涨落定理将正熵和负熵事件的发生设置为严格关系，因此我们能够验证由熵消耗或熵产生定义的级联轨迹如何与湍流结构相关联：具有熵产生的轨迹从大范围的大速度增量开始，并在小规模下收敛到零速度增量；具有熵消耗的轨迹以有限的大小以小比例的速度增量结束，并且对于小比例的增量显示下限。发现负熵值的大小呈线性增加。这表明速度场中局部不连续的趋势。我们的发现没有显示负熵值的下限，因此对于小规模结构的相应堆积速度差异。发现负熵值的大小呈线性增加。这表明速度场中局部不连续的趋势。我们的发现没有显示负熵值的下限，因此对于小规模结构的相应堆积速度差异。发现负熵值的大小呈线性增加。这表明速度场中局部不连续的趋势。我们的发现没有显示负熵值的下限，因此对于小规模结构的相应堆积速度差异。