The affective thermodynamic relationship: an empirical information-theoretic scaling relationship for normative-conflict collapse in large language models

Large language models (LLMs) are increasingly deployed in value-sensitive, normatively ambiguous settings, yet we still lack quantitative characterisations of when alignment fails under normative conflict. Building on a corpus of norm conflict scenarios and more than 9 000 responses across multiple model families, this Article reports an affective thermodynamic relationship , empirically stable across the tested transformer-based model families, linking interpretative collapse, sampling variance, and information-theoretic capacity. First, we show that the probability of normative-collapse λ is well described by a descriptively stable Kramers-like scaling relationship of the form ln \; λ =m\,σ ⁻²+b ln λ = m σ − 2 + b , where σ 2 is an empirically calibrated effective sampling variance; the formulation is phenomenological and rate-based rather than a claim about underlying physical mechanisms. The inferred slope m is statistically indistinguishable across the tested architectures, consistent with an empirically stable fitted slope for the tested families, an approximate scaling regularity rather than a universal alignment constant, that describes the observed collapse pattern under normative conflict. Second, by reparameterising in terms of per-token entropy, we interpret this scaling relationship in terms of a phenomenological information-theoretic capacity bound: collapse probability rises sharply once the information required to preserve normative coherence appears to exceed the effective channel capacity available at a given entropy level. Third, we identify an operational critical region, a collapse-prone corridor in entropy space, that can be approximated by a logistic rate law and that shifts predictably under Junk-Persona Prompt Injection (JPPI), as quantified by an Affective Degradation Index (ADI). Taken together, these results identify a reproducible empirical pattern in the released dataset and support a bounded information-theoretic interpretation for the tested transformer-based families. Because inter-rater reliability for collapse judgements is inherently low in normatively contested settings, and may partly reflect the absence of a single ground truth rather than simple annotation noise, all rate-law relationships reported here should be interpreted as probabilistic measurement–model associations rather than definitive psychometric or ethical laws. We situate the results within broader debates on interpretative failure, human–AI interaction, and governance in AI systems used in value-sensitive or affect-laden interactions.