论文标题
维持温度差
Sustaining a temperature difference
论文作者
论文摘要
我们得出了最低熵率的表达式，该表达式在不同温度下维持两个储层$ t_0 $和$ t_ \ ell $。法律显示了对相对距离和特征$ \ log^2（t_ \ ell/t_0）$依赖性的直观$ \ ell^{ - 1} $依赖关系。首先，我们根据传导的傅立叶定律（FL）给出了回音的论点，表明最小散落的轮廓是指数级的。然后，我们重新审视一个振荡器链的模型，每个振荡器耦合到热储存库。在大型阻尼的极限中，我们重新侵蚀了指数和平方的行为，提供了FL的自洽推导。对于小型阻尼，“焦点挫败感”导致了众所周知的巴利斯行为，其与佛罗里达州的不相容构成了长期挑战。
We derive an expression for the minimal rate of entropy that sustains two reservoirs at different temperatures $T_0$ and $T_\ell$. The law displays an intuitive $\ell^{-1}$ dependency on the relative distance and a characterisic $\log^2 (T_\ell/T_0)$ dependency on the boundary temperatures. First we give a back-of-envelope argument based on the Fourier Law (FL) of conduction, showing that the least-dissipation profile is exponential. Then we revisit a model of a chain of oscillators, each coupled to a heat reservoir. In the limit of large damping we reobtain the exponential and squared-log behaviors, providing a self-consistent derivation of the FL. For small damping "equipartition frustration" leads to a well-known balistic behaviour, whose incompatibility with the FL posed a long-time challenge.
