Thermodynamic Space of Chemical Reaction Networks

Abstract

Living systems operate out of equilibrium, continuously consuming energy to sustain organised, functional states. Their emergent behaviour 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 non-equilibrium driving, can limit local non-equilibrium quantities. We illustrate our results in various paradigmatic examples, demonstrating how the onset of complex behaviors is intimately tangled with the presence of non-equilibrium conditions. By providing a general tool for analysing 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.