Geometry of Nonequilibrium Reaction Networks

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 usually have many-to-many interactions, chemical networks are described by hype...

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Bibliographic Details
Published in:Physical review. X 2023-06, Vol.13 (2), p.021040, Article 021040
Main Authors: Dal Cengio, Sara, Lecomte, Vivien, Polettini, Matteo
Format: Article
Language:English
Subjects:
Condensed Matter
Physics
Statistical Mechanics
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Summary: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 usually have many-to-many interactions, chemical networks are 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 an 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.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.13.021040