Chemical Thermodynamics for Growing Systems

TL;DR

This paper develops a thermodynamic framework for open, growing chemical reaction systems, extending existing theories to include volume change, and identifies conditions for growth, shrinking, or steady states based on the second law of thermodynamics.

Contribution

It introduces a thermodynamic theory for growing CRSs by extending Hessian geometry, providing conditions for their fate and thermodynamic constraints without specific kinetic assumptions.

Findings

Identifies environmental conditions for growth, shrinkage, or equilibrium.

Establishes thermodynamic constraints on growing CRSs.

Evaluates entropy production in steady growing states.

Abstract

We consider growing open chemical reaction systems (CRSs), in which autocatalytic chemical reactions are encapsulated in a finite volume and its size can change in conjunction with the reactions. The thermodynamics of growing CRSs is indispensable for understanding biological cells and designing protocells by clarifying the physical conditions and costs for their growing states. In this work, we establish a thermodynamic theory of growing CRSs by extending the Hessian geometric structure of non-growing CRSs. The theory provides the environmental conditions to determine the fate of the growing CRSs; growth, shrinking or equilibration. We also identify thermodynamic constraints; one to restrict the possible states of the growing CRSs and the other to further limit the region where a nonequilibrium steady growing state can exist. Moreover, we evaluate the entropy production rate in the steady growing state. The growing nonequilibrium state has its origin in the extensivity of thermodynamics, which is different from the conventional nonequilibrium states with constant volume. These results are derived from general thermodynamic considerations without assuming any specific thermodynamic potentials or reaction kinetics; i.e., they are obtained based solely on the second law of thermodynamics.