Atom as an Agent: Emergent Order by Collective Predictive Coding

Simulating societies of many large language model (LLM) agents is expensive, yet the questions asked of such simulations are usually macroscopic: phase behaviour, stylised facts, and scaling with the number of agents $N$, not the cognition of any single agent. We turn a statistical-physics observation into a method: replace each LLM agent by a low-parameter model fitted from a few hundred to a few thousand cheap queries, then run the society at any $N$ on a laptop. Whether this works is decided before the simulation runs, chiefly by what each agent perceives. We introduce an [interaction order x memory] taxonomy that maps perception and memory to an effective theory and a predicted $N$-trend of the surrogate error. We validate it on a faithful reimplementation of the LLM macroeconomy EconAgent and seven further named LLM simulations, with agent decisions cloned from genuine LLM elicitations (primarily DeepSeek) for a few dollars; the predicted error trends hold cell by cell, and the two refuted predictions, both on a strongly saturating response and traced to its curvature, are themselves matched quantitatively by the theory with no free parameters.

We investigate the emergent collective dynamics of LLM-based multi-agent systems on a 2D square lattice and present a model-agnostic statistical-physics method to disentangle social conformity from intrinsic bias, compute critical exponents, and probe the collective behavior and possible phase transitions of multi-agent systems. In our framework, each node of an $L\!\times\!L$ lattice hosts an identical LLM agent holding a binary state ($+1$/$-1$, mapped to yes/no) and updating it by querying the model conditioned on the four nearest-neighbor states. The sampler temperature $T$ serves as the sole control parameter. Across three open-weight models (llama3.1:8b, phi4-mini:3.8b, mistral:7b), we measure magnetization and susceptibility under a global-flip protocol designed to probe $\mathbb{Z}_2$ symmetry. All models display temperature-driven order-disorder crossovers and susceptibility peaks; finite-size scaling on even-$L$ lattices yields effective exponents $γ/ν$ whose values are model-dependent, close to but incompatible with the 2D Ising universality class ($γ/ν=7/4$). Our method enables the extraction of effective $β$-weighted couplings $\tilde{J}(T)$ and fields $\tilde{h}(T)$, which serve as a measure of social conformity and intrinsic bias. In the models we analyzed, we found that collective alignment is dominated by an intrinsic bias ($\tilde{h}\gg\tilde{J}$) rather than by cooperative neighbor coupling, producing field-driven crossovers instead of genuine phase transitions. These effective parameters vary qualitatively across models, providing compact collective-behavior fingerprints for LLM agents and a quantitative diagnostic for the reliability of multi-agent consensus and collective alignment.

According to the theory of constructed emotion, the brain actively forms emotion categories by integrating multimodal bodily signals, and constructs emotional experiences by using these categories to predict and interpret sensory inputs. While research has advanced in modeling individual emotion construction, the social process of co-construction-how a shared understanding of emotions emerges between individuals-remains computationally underexplored. This study investigates this process by modeling emergent communication between two embodied agents using the Metropolis-Hastings Naming Game (MHNG), grounded in the Collective Predictive Coding (CPC) framework. Our experiments, using visual, auditory, and simulated interoceptive inputs, yield two main findings. First, MHNG-based communication significantly improves the alignment, clarity, and inter-agent agreement of the learned emotion categories compared to non-communicative and non-selective baselines, with the alignment effect concentrated at the symbolic layer rather than the perceptual latent representation. Second, even when the two agents have systematically divergent interoceptive dynamics, communication still produces robust categorical alignment, with distinct, category-specific reshaping patterns of each agent's emotion categories-consistent with the constructed-emotion view that interoceptive heterogeneity is constitutive of, rather than an obstacle to, shared emotional meaning. These findings provide computational support for the co-constructionist view of emotion and extend the CPC framework from physical to socially-grounded domains.