Universal properties of the statistics of stochastic efficiency for mesoscopic time-reversal symmetry broken energy transducers are revealed in the Gaussian approximation. We also discuss how the second law of thermodynamics restricts the statistics of stochastic efficiency. The tight-coupling (reversible) limit becomes unfavorable, characterized by an infinitely broad distribution of efficiency at {\em all times}, when time-reversal symmetry breaking leads to an asymmetric Onsager response matrix. The underlying physics is demonstrated through the integer quantum Hall effect and further elaborated in a triple-quantum-dot three-terminal thermoelectric engine.
Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's $\hat K$ matrices for networks with broken time reversal invariance
我们提出了一个广泛的实验研究的散射矩阵$\hat S$和Wigner的反应$\hat K$ -矩阵的非对角元素的实部和虚部的分布与破缺时间（$T$）反转不变性的开放微波网络。为了打破$T$不变性，应用了微波法拉第循环器。将散射矩阵$\hat S$非对角元实部和虚部的实验分布与超对称随机矩阵理论[A. Nock，S. Kumar，H.- J. Sommers和T. Guhr，Annals of Physics { \bf 342}，103-132（2014）]。此外，我们还证明了实验结果与最近在随机矩阵理论（RMT）的高斯幺正系综框架内得到的Wigner反应$\hat K$ -矩阵的非对角元素实部和虚部分布的预测非常一致[S. B. Fedeli和Y. V. Fyodorov，J. Phys. A：Math. Theor. { \bf 53}，165701（2020）]。这两种理论都包括损耗作为可调参数，因此很好地适应了实验验证。
