Physical computing systems provide a promising route toward hardware-native machine learning, but their computational capabilities remain difficult to characterize in a principled, task-independent, and data-efficient way. We extend the Information Processing Capacity (IPC) framework to stationary physical computing systems and establish several fundamental results: individual capacities are bounded between zero and one, their sum over a complete basis is bounded by the number of readouts, and noise strictly reduces this bound. We address the finite-sample estimation of IPC and derive the asymptotic form of the systematic positive bias affecting naive estimators. Building on these results, we introduce data-efficient estimation methods based on Richardson extrapolation and Sobol quasi-random sampling. We validate the framework experimentally using a photonic computing system based on picosecond laser pulses propagating through a nonlinear optical fibre. By varying the laser power and fibre length, we observe systematic shifts of the IPC distribution toward higher-order nonlinear capacities induced by the Kerr effect. Finally, we demonstrate that the total IPC strongly correlates with performance on benchmark machine-learning tasks and provides a reliable estimate of the effective dimensionality of the system. These results establish IPC as a practical bridge between the intrinsic dynamics of physical computing systems and their machine-learning performance.

翻译：物理计算系统为硬件原生机器学习提供了一条有前景的路径，但其计算能力仍难以在原则性、任务无关且数据高效的方式下进行表征。我们将信息处理容量(IPC)框架扩展至静态物理计算系统，并建立了若干基础性结果：单个容量值介于0与1之间，其在完备基上的总和受读出数量限制，而噪声会严格降低这一总和。我们解决了IPC的有限样本估计问题，推导了影响朴素估计器的系统正偏差的渐近形式。基于这些结果，我们引入了基于理查森外推法和Sobol准随机抽样的数据高效估计方法。我们利用基于皮秒激光脉冲在非线性光纤中传播的光子计算系统，对框架进行了实验验证。通过改变激光功率和光纤长度，我们观察到由克尔效应引发的IPC分布向高阶非线性容量的系统性迁移。最后，我们证明了总IPC与基准机器学习任务的表现强相关，并为系统有效维度提供了可靠估计。这些结果确立了IPC作为连接物理计算系统内在动力学与机器学习性能之间的实用桥梁。