Thermodynamic Space of Chemical Reaction Networks
Abstract
Living systems operate out of equilibrium, continuously consuming energy to sustain organized, functional states. Their emergent behavior usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes that keep some species at fixed concentrations. Hence, uncovering the principles governing the functioning of these CRNs is crucial to understand how living systems generate and regulate complexity. While kinetics plays a key role in shaping detailed dynamical phenomena, the range of operations of a CRN is fundamentally constrained by thermodynamics. Here, we introduce and analytically derive the “thermodynamic space” of a CRN, i.e., the range of accessible stationary concentrations that can be realized under a given energetic budget. We establish analogous bounds for reaction affinities, shedding light on how global thermodynamic properties, such as the total nonequilibrium driving, can limit local nonequilibrium quantities, and further showing that these bounds can be used to test candidate network topologies and expose hidden multimolecular pathways. We illustrate our results in various paradigmatic examples, demonstrating how the onset of complex behaviors is intimately tangled with the presence of nonequilibrium conditions. By providing a general tool for analyzing CRNs, the presented framework constitutes a stepping stone to deepen our ability to predict complex out-of-equilibrium phenomena and design artificial chemical systems, starting from the sole knowledge of the underlying thermodynamic properties.
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BibTeX
@article{梁师翎2026thermodynamic,
title = {{Thermodynamic Space of Chemical Reaction Networks}},
author = {Shiling Liang (梁师翎) and Paolo De Los Rios and Daniel Maria Busiello},
journal = {Physical Review X},
year = {2026},
month = oct,
doi = {10.1103/g875-ldn5},
url = {http://link.aps.org/doi/10.1103/g875-ldn5},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Thermodynamic Space of Chemical Reaction Networks
AU - Shiling Liang (梁师翎)
AU - Paolo De Los Rios
AU - Daniel Maria Busiello
PY - 2026
DA - 2026/10/26
JO - Physical Review X
DO - 10.1103/g875-ldn5
UR - http://link.aps.org/doi/10.1103/g875-ldn5
AB - Living systems operate out of equilibrium, continuously consuming energy to sustain organized, functional states. Their emergent behavior usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes that keep some species at fixed concentrations. Hence, uncovering the principles governing the functioning of these CRNs is crucial to understand how living systems generate and regulate complexity. While kinetics plays a key role in shaping detailed dynamical phenomena, the range of operations of a CRN is fundamentally constrained by thermodynamics. Here, we introduce and analytically derive the “thermodynamic space” of a CRN, i.e., the range of accessible stationary concentrations that can be realized under a given energetic budget. We establish analogous bounds for reaction affinities, shedding light on how global thermodynamic properties, such as the total nonequilibrium driving, can limit local nonequilibrium quantities, and further showing that these bounds can be used to test candidate network topologies and expose hidden multimolecular pathways. We illustrate our results in various paradigmatic examples, demonstrating how the onset of complex behaviors is intimately tangled with the presence of nonequilibrium conditions. By providing a general tool for analyzing CRNs, the presented framework constitutes a stepping stone to deepen our ability to predict complex out-of-equilibrium phenomena and design artificial chemical systems, starting from the sole knowledge of the underlying thermodynamic properties.
SN - 2160-3308
ER -