Kinetics and thermodynamics of reversible polymerization in closed systems

TL;DR

This paper investigates the kinetics and thermodynamics of reversible polymerization in closed systems, establishing a thermodynamic framework that links nonequilibrium dynamics with equilibrium properties, applicable to various conservation scenarios.

Contribution

It introduces a comprehensive thermodynamic formulation for reversible polymerization, connecting Lyapunov functions with entropy production and extending to systems with or without solvent inclusion.

Findings

Lyapunov function as Kullback-Leibler divergence between distributions

System evolves towards equilibrium satisfying detailed balance

Thermodynamic quantities can be dynamically tracked during polymerization

Abstract

Motivated by a recent work on the metabolism of carbohydrates in bacteria, we study the kinetics and thermodynamics of two classic models for reversible polymerization, one preserving the total polymer concentration and the other one not. The chemical kinetics is described by rate equations following the mass-action law. We consider a closed system and nonequilibrium initial conditions and show that the system dynamically evolves towards equilibrium where detailed balance is satisfied. The entropy production during this process can be expressed as the time derivative of a Lyapunov function. When the solvent is not included in the description and the dynamics conserves the total concentration of polymer, the Lyapunov function can be expressed as a Kullback-Leibler divergence between the nonequilibrium and the equilibrium polymer length distribution. The same result holds true when the solvent is explicitly included in the description and the solution is assumed dilute, whether or not the total polymer concentration is conserved. Furthermore, in this case a consistent nonequilibrium thermodynamic formulation can be established and the out-of-equilibrium thermodynamic enthalpy, entropy and free energy can be identified. Such a framework is useful in complementing standard kinetics studies with the dynamical evolution of thermodynamic quantities during polymerization.