Information Creation as Retained Correlation: A Kinetic Framework for the Emergence of Collective Dynamics

Emergence—collective behaviour that no element of a system has on its own—lacks a dynamical mechanism that says which variable carries it, why descriptions of the parts cannot see it, and when it begins. We propose one by connecting information theory, which quantifies statistical dependence, with kinetic theory, which describes how distributions and correlations evolve:

correlations generated by interactions can be retained by a system and returned through its dynamics, thereby changing collective behaviour. The proposed mechanism has three operations—writing, retention and read-back—and is formulated first at the level of a hierarchy of distribution functions, then reduced to a minimal activity–correlation model. For a neural population, the pair distribution is decomposed into an independent part and a connected pair correlation, f_2= f_1f_1+ g_2. The mutual information between two units is the Kullback–Leibler divergence of the joint distribution from the product of its marginals; it is non-negative and vanishes exactly at independence. In the weak-correlation regime it is quadratic, rather than linear, in the connected correlation. What emerges is therefore correlation information, a property of the pair and of neither unit, and it is invisible to every factorised description, which sets g_2 to zero. Retaining g_2 in the kinetic description and eliminating it produces a memory kernel in the activity dynamics. For an opposite-sign read-back the reduced operator has an exceptional point beyond which a collective mode appears that no single unit carries: the onset of emergence is calculated, not assumed. Three measurable conditions follow—the mode is carried by correlation, the correlation is retained and read back, and the population has a frequency its units lack—together with interventions that test each of them.

Keywords:  emergence · causality · information theory · complex networks · neural networks· statistical mechanics · Boltzmann transport equation · molecular chaos · critical exponents  · Kullback-Leibler divergence · free energy principle · Landauer principle · self-modeling systems · neuromorphic computing.