The concept of autonomy is fundamental for understanding biological organization and the evolutionary transitions of living systems. Understanding how a system constitutes itself as an individual, cohesive, self-organized entity is a fundamental challenge for the understanding of life. However, it is generally a difficult task to determine whether the system or its environment has generated the correlations that allow an observer to trace the boundary of a living system as a coherent unit. Inspired by the framework of integrated information theory, we propose a measure of the level of integration of a system as the response of a system to partitions that introduce perturbations in the interaction between subsystems, without assuming the existence of a stationary distribution. With the goal of characterizing transitions in integrated information in the thermodynamic limit, we apply this measure to kinetic Ising models of infinite size using mean field techniques. Our findings suggest that, in order to preserve the integration of causal influences of a system as it grows in size, a living entity must be poised near critical points maximizing its sensitivity to perturbations in the interaction between subsystems. Moreover, we observe how such a measure is able to delimit an agent and its environment, being able to characterize simple instances of agent-environment asymmetries in which the agent has the ability to modulate its coupling with the environment.