Abstract
When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available energy, might be dominant in dictating the stationary populations of all chemical states out of equilibrium. This phenomenology has been theoretically explored mainly in the infinite diffusion limit. Here, we show that the regime in which the diffusion rate is finite, and also slower than some chemical reactions, might bring about interesting features, such as the maximisation of selection or the switch of the selected state at stationarity. We introduce a framework, rooted in a time-scale separation analysis, which is able to capture leading non-equilibrium features using only equilibrium arguments under well-defined conditions. In particular, it is possible to identify fast-dissipation sub-networks of reactions whose Boltzmann equilibrium dominates the steady-state of the entire system as a whole. Finally, we also show that the dissipated heat (and so the entropy production) can be estimated, under some approximations, through the heat capacity of fast-dissipation sub-networks. This work provides a tool to develop an intuitive equilibrium-based grasp on complex non-isothermal reaction networks, which are important paradigms to understand the emergence of complex structures from basic building blocks.
Highlights
Substituting the steady-state solutions obtained from Equation (12) in Equation (24), indicated above as Ptheory ( X ) for simplicity, we derive a theoretically approximated version of the entropy production which is valid when the diffusion coefficient is in a desired intermediate range
Another experimentally feasible way to introduce a temperature gradient is to put the chemical system in contact with a heat bath whose temperature is periodically changed over time
This turns out to be easier than applying a steady thermal gradient [27,28]
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Recent works [11,12] have studied the consequences of applying a thermal gradient to a diffusive chemical system They elucidated that non-equilibrium conditions couple with an underlying kinetic asymmetry in the transition rates, favouring, at stationarity, a subset of chemical states that are unfavourable at equilibrium [13]. We find that it is possible to achieve higher selection than in the fast diffusion limit, as well as an inversion in the state that will be selected at stationarity This complex picture can be captured by a time-scale separation analysis under some approximations, and, as a consequence, we find that appropriate local equilibrium predictions can give precious hints to rephrase and understand these non-equilibrium behaviours
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