论文标题
随机线积分和流充当不可逆性和传热的指标
Stochastic line integrals and stream functions as metrics of irreversibility and heat transfer
论文作者
论文摘要
随机线积分为定量表征不可逆性和详细的平衡违规提供了有用的工具。一个特殊的认识是随机区域，最近在耦合电路中研究了。在这里，我们提供了一个一般框架，以了解随机线积分的属性，并阐明它们在实验和模拟中的实现。对于二维系统，随机线积分可以用流函数表示，其符号决定了稳态概率电流的方向。此外，流函数允许对随机区域对关键参数的缩放依赖性的分析理解，例如非线性和线性弹簧的噪声强度。理论上的结果得到了导致均衡驱动的二维质量弹力系统的数值研究支持。
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled electrical circuits. Here, we provide a general framework for understanding properties of stochastic line integrals and clarify their implementation for experiments and simulations. For two-dimensional systems, stochastic line integrals can be expressed in terms of a stream function, the sign of which determines the orientation of steady-state probability currents. Additionally, the stream function permits analytical understanding of the scaling dependence of stochastic area on key parameters such as the noise strength for both nonlinear and linear springs. Theoretical results are supported by numerical studies of an overdamped, two-dimensional mass-spring system driven out of equilibrium.
