Opinion Dynamics Entropy Generation via Complex Network Structures*

Sociophysics is a compelling and dynamic research field that leverages the principles of physics and sociology to delve into collective behaviors, such as the dynamics of opinions, misinformation spread, financial crises, and political radicalization. Recent scientific investigations have uncovered the role of entropy production in the intricate dynamics of collective systems, fundamental processes underpinning phase transitions, and polarization. The majority-vote model stands out as a straightforward framework for elucidating the dynamics of group opinions in elections, debates, and financial markets. In this model, each individual holds one of two opinions on a given subject, influenced by their social connections. A parameter q introduces a social anxiety capacity, enabling a behavioral social disorder. With probability (1-q), individuals tend to conform to the prevailing opinion within their social interaction network, while with chance q, they act in nonconformity. This work explores the social entropy production of majority-vote opinion dynamics in complex networks, including Erdös-Rényi random graphs, scale-free and small-world networks via Monte Carlo simulations and mean-field analysis.