# Kinetics and thermodynamics of reversible polymerization in closed systems

Source: [Kinetics and thermodynamics of reversible polymerization in closed systems](<https://www.sota2.com/research/paper/68fa324c1e209131ce886f87>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:37:49.778Z

Authors: Sourabh Lahiri, Yang Wang, Massimiliano Esposito, David Lacoste

Published: 2015-06-17T16:16:12.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1506.05377>)

[PDF](<https://arxiv.org/pdf/1506.05377.pdf>)