论文标题
非平衡反应网络的状态空间重新归一化群体理论：在任意维度中的超顺从晶格的精确解决方案
State-space renormalization group theory of nonequilibrium reaction networks: Exact solutions for hypercubic lattices in arbitrary dimensions
论文作者
论文摘要
大多数生物学功能是非平衡反应网络（NRN）。尽管具有多种动态特性，但NRN具有持续概率通量和连续耗能的标志性特征，即使在稳定状态下也是如此。可以在不同的粗粒水平上描述NRN的动力学。我们以前的工作表明，粗粒水平的表观耗散速率遵循了对粗粒度尺度的反功率定律。缩放指数取决于固定概率通量的网络结构和相关性。然而，尚不清楚（重新归一化的）通量相关性是否随粗晶粒而变化。遵循Kadanoff对关键现象的真实空间重新归一化组（RG）方法，我们通过为NRN开发一个状态空间重新归一化组（SSRG）理论来解决这个问题，该理论为通量相关功能提供了迭代的RG方程。在方形和超管晶格中，我们精确地求解了RG方程，并找到了两种类型的固定点解：一个非平凡固定点的家族，相关性表现出幂律衰减和相关性在最近的邻居以外消失的微不足道的固定点。且仅当功率指数小于晶格尺寸$ n $时，幂律固定点才稳定。因此，仅当细粒网络中的相关性衰减慢于$ r^{ - n} $时，相关函数才会收敛到power-law固定点。如果细粒网络中的通量相关性包含带有不同指数的多个稳定解，则RG迭代动力学选择具有最小指数的固定点解。我们还讨论了通量相关的RG流与kosterlitz的RG流之间的可能联系。
Nonequilibrium reaction networks (NRNs) underlie most biological functions. Despite their diverse dynamic properties, NRNs share the signature characteristics of persistent probability fluxes and continuous energy dissipation even in the steady state. Dynamics of NRNs can be described at different coarse-grained levels. Our previous work showed that the apparent energy dissipation rate at a coarse-grained level follows an inverse power law dependence on the scale of coarse-graining. The scaling exponent is determined by the network structure and correlation of stationary probability fluxes. However, it remains unclear whether and how the (renormalized) flux correlation varies with coarse-graining. Following Kadanoff's real space renormalization group (RG) approach for critical phenomena, we address this question by developing a State-Space Renormalization Group (SSRG) theory for NRNs, which leads to an iterative RG equation for the flux correlation function. In square and hypercubic lattices, we solve the RG equation exactly and find two types of fixed point solutions: a family of nontrivial fixed points where the correlation exhibits power-law decay and a trivial fixed point where the correlation vanishes beyond the nearest neighbors. The power-law fixed point is stable if and only if the power exponent is less than the lattice dimension $n$. Consequently, the correlation function converges to the power-law fixed point only when the correlation in the fine-grained network decays slower than $r^{-n}$ and to the trivial fixed point otherwise. If the flux correlation in the fine-grained network contains multiple stable solutions with different exponents, the RG iteration dynamics select the fixed point solution with the smallest exponent. We also discuss a possible connection between the RG flows of flux correlation with those of the Kosterlitz-Thouless transition.
