Hessian geometry of nonequilibrium chemical reaction networks and entropy production decompositions
Hessian geometry of nonequilibrium chemical reaction networks and entropy production decompositions
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DOI：
10.1103/physrevresearch.4.033208
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发表时间：
2022-09
影响因子：
4.2
通讯作者：
Tetsuya J. Kobayashi;Dimitri Loutchko;A. Kamimura;Yuki Sughiyama
中科院分区：
文献类型：
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作者：
Tetsuya J. Kobayashi;Dimitri Loutchko;A. Kamimura;Yuki Sughiyama
我们推导了非平衡化学反应网络在凸耗散函数的勒让德对偶诱导的通量空间和力空间上的Hessian几何结构，并将其动力学特征描述为广义流。有了这种几何结构，我们可以将具有二次耗散函数的非平衡系统的理论扩展到更一般的非二次耗散系统，这对于研究化学反应网络是至关重要的。通过将Hessian几何中的广义正交性概念应用于化学反应网络，得到了熵产生率的两个广义分解，每个分解都捕获了非平衡动力学中的梯度流和最小耗散方面。
We derive the Hessian geometric structure of nonequilibrium chemical reaction networks on the flux and force spaces induced by the Legendre duality of convex dissipation functions and characterize their dynamics as a generalized flow. With this geometric structure, we can extend theories of nonequilibrium systems with quadratic dissipation functions to more general cases with nonquadratic ones, which are pivotal for studying chemical reaction networks. By applying generalized notions of orthogonality in Hessian geometry to chemical reaction networks, two generalized decompositions of the entropy production rate are obtained, each of which captures gradient-flow and minimum-dissipation aspects in nonequilibrium dynamics.