论文标题
非平衡反应网络的几何形状
Geometry of nonequilibrium reaction networks
论文作者
论文摘要
离散系统的现代热力学基于图理论，该理论既提供了定义可观察物的代数方法，也提供了其含义和作用的几何直觉。但是，由于化学反应通常是多到人类的，因此化学网络被高图形绘制而成，后者缺乏系统化的代数处理和明确的几何直觉。在这里，我们通过构建化学周期（编码固定行为）和Cocycles（编码有限时间放松）的基本基础来填补这一空白。我们用超图上的循环和梯度来解释它们，并使用它们正确识别非平衡观测值。作为应用，我们在线性响应中揭示了隐藏的对称性，并在此制度内提出了一种与Kirchhoff的电压和当前定律一致的大型代谢网络的重建算法。
The modern thermodynamics of discrete systems is based on graph theory, which provides both algebraic methods to define observables and a geometric intuition of their meaning and role. However, because chemical reactions are usually many-to-many, chemical networks are rather described by hypergraphs, which lack a systematized algebraic treatment and a clear geometric intuition. Here we fill this gap by building fundamental bases of chemical cycles (encoding stationary behavior) and cocycles (encoding finite-time relaxation). We interpret them in terms of circulations and gradients on the hypergraph, and use them to properly identify nonequilibrium observables. As application, we unveil hidden symmetries in linear response and, within this regime, propose a reconstruction algorithm for large metabolic networks consistent with Kirchhoff's Voltage and Current Laws.
