Applying Stochastic Thermodynamics to Sociophysics

ABSTRACT
The development of stochastic thermodynamics during the last decades prompted the discovery of novel non-equilibrium 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. In this double talk, we will argue that such question can be answered in the positive. by discussing two recent applications of the framework in the context of social systems, namely (i) the imitation dynamics of opinions and social traits, and (ii) the process of commuting between home and work in the context of urban mobility.
In the first part, presented by Prof. Gonzalo Manzano, we will discuss, how stochastic thermodynamics allows for the formulation of 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. In this context cornerstone results—fluctuation theorems, kinetic and thermodynamic uncertainty relations, and second-law-like inequalities—emerge naturally, and reveal fundamental trade-offs in opinion currents arising from the competition between herding and anti-conformity, and providing inference tools.
In the second part, presented by Mr. Lucas Trigal, we will introduce a related framework interpreting home-to-work movement in cities as a Markov process. Applying the notion of entropy production from stochastic thermodynamics, we quantify how individual trips, urban areas, and entire cities contribute to the irreversible structure of daily mobility. Applied to U.S. cities, the method shows how the entropy production is intimately connected to the density of cities, the prevalence of unidirectional commuting flows, the spectral gap of the commuting network, and the heterogeneity of workplace population distributions.