标题： 物理网络的线性响应统一模型 显示英文标题

标题： A unified model for linear responses of physical networks

摘要： 许多物理系统——从机械晶格和电气电路到生物组织和设计超材料——可以被理解为传输物理量的网络。 我们提出了一种统一的数学框架，使用代数图论工具来描述此类物理网络的线性响应。 这种方法利用节点和边变量（例如，电势、流量）跨多个领域（包括机械、电气、热和扩散响应）捕捉静态和动态行为。 我们的形式化方法将多尺度和多领域响应与底层网络结构联系起来。 我们展示了这个框架如何能够高效地解决一系列线性响应问题，包括应力传播、电荷传输和波动力学，并提供了关于网络对偶性和熵产生的见解。 显示英文摘要

摘要： Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for describing linear responses of such physical networks using tools from algebraic graph theory. This approach captures static and dynamic behaviors across multiple domains, including mechanical, electrical, thermal, and diffusive responses using node and edge variables (e.g., potentials, flows). Our formalism connects multiscale and multi-domain responses to the underlying network structure. We demonstrate how this framework enables efficient, generalizable solutions to a wide class of linear response problems, including stress propagation, charge transport, and wave dynamics, and provide insights into network duality and entropy production.