The development of stochastic thermodynamics during the last decades prompted the discovery of novel nonequilibrium relations refining our understanding of the second law in small fluctuating systems and its connection with information theory. A fundamental open question is whether these powerful tools can illuminate other areas of complex systems, such as social phenomena, where energy plays no fundamental role. Here we develop a framework that derives a ``second law" for social systems. Similarly to Landauer's principle, it constrains spontaneous changes in agent attributes (opinions, cultural traits, etc.) and their informational entropy. We apply this framework to toy agent-based models of social imitation with non-trivial phase diagrams. We demonstrate how cornerstone results -- fluctuation theorems, kinetic and thermodynamic uncertainty relations, and second-law-like inequalities -- emerge naturally in this context, even across symmetry-breaking transitions. These results reveal fundamental trade-offs in opinion currents arising from the competition between herding and anti conformity. Moreover, they provide inference tools to extract model parameters from observations of stochastic changes in agents.