Dynamically-Stable Low-Entropy Solutions: from Thermo- to Infodynamics of Differentiated Adaptation

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Abstract
Open, strongly non-equilibrium systems subject to sustained fluxes of energy, matter, and entropy can, at times and under specific conditions, exhibit transitions to dynamically stable, low-entropy configurations. Such states are empirically observed yet demonstrably rare, suggesting they emerge not from general organizing principles but as particular solutions permitted by system dynamics and boundary constraints. This study examines the conditions under which thermodynamic transitions arising stochastically lead to internal differentiation with respect to essential environmental variables. Differentiation is shown to increase both the structural complexity of the system and its informational fitness, measured in terms of mutual information with relevant external distributions. Through a physically motivated example, we demonstrate how such transitions can yield higher-order configurations exhibiting differentiated response, increased persistence, and adaptive potential. On this basis, we propose a formulation of informational dynamics: a theoretical framework describing the emergence and evolution of internal informational structure in systems under thermodynamic constraints and physical laws of open non-equilibrium systems. Infodynamics seeks to characterize adaptation via differentiation in terms of information-theoretic relations abstracting from specific physical substrates while preserving essential constraints imposed by the environment and the system’s thermodynamic embedding.

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