Nonequilibrium thermodynamic signatures of collective dynamical states around chimera in a chemical reaction network

TL;DR

This paper investigates the nonequilibrium thermodynamic signatures of various collective dynamical states, including chimera states, in a chemical reaction network modeled by a modified complex Ginzburg-Landau equation, revealing thermodynamic markers and relationships.

Contribution

It introduces a systematic thermodynamic characterization of collective states in a chemical oscillator system, linking thermodynamic profiles with dynamical states and transitions.

Findings

Spatial entropy production profiles differ across states.

Thermodynamic signatures reveal state exclusiveness and similarities.

A relationship between thermodynamic potential and activator concentration variance is established.

Abstract

Different dynamical states ranging from coherent, incoherent to chimera, multichimera, and related transitions are addressed in a globally coupled nonlinear continuum chemical oscillator system by implementing a modified complex Ginzburg-Landau equation. Besides dynamical identifications of observed states using standard qualitative metrics, we systematically acquire nonequilibrium thermodynamic characterizations of these states obtained via coupling parameters. The nonconservative work profiles in collective dynamics qualitatively reflect the time-integrated concentration of the activator, and the majority of the nonconservative work contributes to the entropy production over the spatial dimension. It is illustrated that the evolution of spatial entropy production and semigrand Gibbs free energy profiles associated with each state are connected yet completely out of phase, and these thermodynamic signatures are extensively elaborated to shed light on the exclusiveness and similarities of these states. Moreover, a relationship between the proper nonequilibrium thermodynamic potential and the variance of activator concentration is established by exhibiting both quantitative and qualitative similarities between a Fano factor-like entity, derived from the activator concentration, and the Kullback-Leibler divergence associated with the transition from a nonequilibrium homogeneous state to an inhomogeneous state. Quantifying the thermodynamic costs for collective dynamical states would aid in efficiently controlling, manipulating, and sustaining such states to explore the real-world relevance and applications of these states.