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Different dynamical states ranging from coherent, incoherent to chimera,multichimera, and related transitions are addressed in a globally couplednonlinear continuum chemical oscillator system by implementing a modifiedcomplex Ginzburg-Landau equation. Besides dynamical identifications of observedstates using standard qualitative metrics, we systematically acquirenonequilibrium thermodynamic characterizations of these states obtained viacoupling parameters. The nonconservative work profiles in collective dynamicsqualitatively reflect the time-integrated concentration of the activator, andthe majority of the nonconservative work contributes to the entropy productionover the spatial dimension. It is illustrated that the evolution of spatialentropy production and semigrand Gibbs free energy profiles associated witheach state are connected yet completely out of phase, and these thermodynamicsignatures are extensively elaborated to shed light on the exclusiveness andsimilarities of these states. Moreover, a relationship between the propernonequilibrium thermodynamic potential and the variance of activatorconcentration is established by exhibiting both quantitative and qualitativesimilarities between a Fano factor-like entity, derived from the activatorconcentration, and the Kullback-Leibler divergence associated with thetransition from a nonequilibrium homogeneous state to an inhomogeneous state.Quantifying the thermodynamic costs for collective dynamical states would aidin efficiently controlling, manipulating, and sustaining such states to explorethe real-world relevance and applications of these states.

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