The single-parameter scaling hypothesis relating the average and variance of the logarithm of the conductance is a pillar of the theory of electronic transport. We use a maximum-entropy ansatz to explore the logarithm of the particle, or energy density $ln\mathcal{W}\left(x\right)$ at a depth $x$ into a random one-dimensional system. Single-parameter scaling would be the special case in which $x=L$ (the system length). We find the result, confirmed in microwave measurements and computer simulations, that the average of $ln\mathcal{W}\left(x\right)$ is independent of $L$ and equal to $-x/\ell$, with $\ell$ the mean free path. At the beginning of the sample, $\mathrm{var}[ln\mathcal{W}(x\left)\right]$ rises linearly with $x$ and is also independent of $L$, with a sublinear increase and then a drop near the sample output. At $x=L$ we find a correction to the value of $\mathrm{var}[lnT]$ predicted by single-parameter scaling.

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一维无序系统中的单参数缩放和最大熵：理论和实验

与电导对数的平均值和方差相关的单参数缩放假设是电子传输理论的基础。我们使用最大熵ansatz探索粒子的对数或能量密度$ln\mathcal{w\; ^}（X）$ 深处 $X$进入一个随机的一维系统。单参数缩放将是其中的特殊情况$X=\mathrm{大号}$（系统长度）。我们发现，在微波测量和计算机模拟中得到的结果是，$ln\mathcal{w\; ^}（X）$ 独立于 $\mathrm{大号}$ 等于 $-X/\ell$， 和 $\ell$平均自由路径。在示例的开头，$\mathrm{变种}[ln\mathcal{w\; ^}（X）]$ 与线性上升 $X$ 并且也独立于 $\mathrm{大号}$，次线性增加，然后在样本输出附近下降。在$X=\mathrm{大号}$ 我们发现对的值进行了更正 $\mathrm{变种}[lnŤ]$ 通过单参数缩放预测。