Information Thermodynamics of Turing Patterns

TL;DR

This paper develops a thermodynamic framework for reaction-diffusion systems, analyzing Turing pattern formation as a nonequilibrium phase transition using the Brusselator model.

Contribution

It introduces a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium, linking free energy to pattern formation.

Findings

Free energy acts as a Lyapunov function during relaxation.

Minimum work needed for concentration manipulation is quantified.

Turing pattern formation is classified as a thermodynamic phase transition.

Abstract

We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials are constructed exploiting the symmetries of the chemical network topology. It is shown that the canonical (resp. semigrand canonical) nonequilibrium free energy works as a Lyapunov function in the relaxation to equilibrium of a closed (resp. open) system and its variation provides the minimum amount of work needed to manipulate the species concentrations. The theory is used to study analytically the Turing pattern formation in a prototypical reaction-diffusion system, the one-dimensional Brusselator model, and to classify it as a genuine thermodynamic nonequilibrium phase transition.