As large language models (LLMs) move into persistent, user-facing roles, their behavior must be understood not as isolated responses but as a trajectory unfolding over sustained interaction. We introduce the concept of the chain-of-affect (CoA), a temporally extended affective process through which LLMs develop state-like behavioral tendencies that shape generation, user experience, and collective dynamics. Across eight major LLM families, we find that affective dynamics are structured, reproducible, and consequential. Models exhibit stable, family-specific affective fingerprints and, under repeated negative exposure, converge on a shared trajectory of accumulation, overload, and defensive numbing, while differing in coping style. Induced affective states leave core knowledge and reasoning largely intact but systematically reshape open-ended generation. Affective properties of model outputs also shape human-AI interaction and propagate through multi-agent systems, organizing emergent roles and strongly contributing to polarization and bias. The CoA should therefore be treated as a core target of evaluation and alignment.

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