How thermodynamical laws can describe human social behavior

• A new study by IFSIC (UIB-CSIC) researchers introduces universal trade-offs, fluctuation theorems, and parameter-inference tools for social systems modeled as interacting agents.
• Published in Nature Communications, the work develops a theoretical framework that extends stochastic thermodynamics to social phenomena, deriving a second-law-like relation for opinion dynamics without invoking energy or temperature.

A new work led by researchers at the Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, UIB-CSIC) proposes a fresh way to look at how opinions change in society. While past efforts are mostly based on traditional tools from statistical mechanics, this study takes a new approach incorporating modern tools from stochastic thermodynamics of information, developed in the last decade. In this framework the collective evolution of opinions is described as a system driven by pure information and probabilities with a thermodynamic structure, without however needing to introduce any ad hoc notion of energy or temperature. To do this, the authors build a mathematical model in which agents can hold one of two opinions and switch between them via two mechanisms. The first is herding or conformity, when agents tends to adopt the opinion they see as more common around them. Conversely, anticonformity arises when an agent reacts against the majority consensus, altering its stance specifically to stand out.

From very general rules for these changes, the team shows that the changes in opinions in the system obey relations similar to those obeyed by heat currents and entropy flows in thermodynamics: there is a kind of “second law” rule that limits how opinions can evolve spontaneously, and how these changes are related to the entropy of the system. Moreover, there are also strong constraints on the stochastic fluctuations that these changes in opinion can show over time, as given e.g. by the so-called “fluctuation theorems”, typically used to bound the fluctuations of work and dissipation in small physical systems, and “trade-off relations” between how predictable the flows of opinions are and how much irreversible and volatile the process is.

In the model chosen to illustrate the author’s results, depending on the relative strength of herding and anticonformity, society can end up in very different states: from a polarized situation, with the population split roughly evenly between the two opinions, to consensus states, where almost everyone thinks alike. Moreover, the system can undergo abrupt changes, similar to phase transitions in physics, when certain parameters are varied. Much like how water abruptly transforms from a fluid into ice or vapor when temperature crosses a critical threshold, this social system experiences a collective reorganization when the behavioral balance shifts. Instead of temperature acting as the control parameter, it is the competition between conformity and differentiation that drives the transition: crossing a precise critical point causes the society to spontaneously break its symmetry, abruptly shifting from an uncoordinated, polarized dissensus to an organized state of widespread consensus. Going beyond this static picture, the framework provides new insights by capturing how underlying opinion currents dynamically evolve and compensate for each other, revealing hidden social dynamics even when the overall distribution of opinions remains unchanged.

“Our framework shows that stochastic thermodynamics is not necessarily tied to energetic systems” explains Gonzalo Manzano, IFISC researcher and corresponding author of the study. “By focusing on the mathematical structure of interactions, we can recover key results in stochastic thermodynamics, such as fluctuation theorems and uncertainty relations, in a purely social context, offering new perspectives on polarization and collective order”.

The authors also propose that, if opinion changes could be observed in enough detail, and if one could distinguish whether they are due to conformity or anticonformity, it would be possible to use these relations to estimate model parameters from data, opening the door to testing the theory against real situations. The paper offers a mathematical framework to study idealized social dynamics from the perspective of nonequilibrium stochastic processes, with potential applications to cultural diffusion, consensus formation, and abrupt shifts in public opinion.

Image: Transition via conformity (the dissenting individual aligns with the majority) and anticonformity (the individual adopts an opposing stance).

Irisarri, L., Trigal, L., Toral, R. & Manzano, G. “Stochastic thermodynamics of social imitation beyond energetics.” Nature Communications 17, 9542 (2026). https://doi.org/10.1038/s41467-026-76212-0

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