We introduce thermodynamic networks, a general framework for autonomous, physics-based computation using non-equilibrium steady states. These networks are modeled as a collection of finite-size reservoirs that exchange conserved quantities--such as electric charge or molecular number--while relaxing to a non-equilibrium steady state, which encodes the solution of a computational problem. We identify Negative Differential Conductance (NDC) as the critical physical property governing the computational expressivity of the thermodynamic network. While networks lacking NDC are restricted to computing monotonic functions, the presence of NDC enables universal function approximation. For the training of the network, we use protocols that take advantage of the natural tendency of the system to equilibrate. We illustrate the versatility of our approach via two different platforms: quantum dot networks and enzymatic reaction networks. Both systems can be engineered to have NDC, enabling high performance in standard benchmarks, including sine function approximation and MNIST digit classification. Overall, our work establishes a rigorous link between non-equilibrium steady states and computational expressivity.

翻译：我们提出热力学网络（thermodynamic networks），这是一个基于非平衡稳态实现自主物理计算的一般框架。这些网络被建模为有限尺寸储层的集合，它们在弛豫到编码计算问题解的非平衡稳态的过程中，交换守恒量（如电荷或分子数）。我们识别出负微分电导（NDC）是控制热力学网络计算表达能力的关键物理特性。缺乏NDC的网络仅限于计算单调函数，而NDC的存在则能够实现通用函数逼近。对于网络训练，我们利用系统自然趋向平衡的特性设计训练协议。通过两种不同平台——量子点网络和酶促反应网络——展示了我们方法的通用性。这两个系统均可设计出NDC特性，从而在标准基准测试中实现高性能，包括正弦函数逼近和MNIST数字分类。总体而言，我们的工作在非平衡稳态与计算表达能力之间建立了严格的理论联系。