Using stochastic thermodynamics to analyze non-thermodynamic properties of networked dynamical systems

Social networks of political voters, gene regulatory networks, recurrent neural networks or groups of flocking birds, all are examples of out-of-equilibrium systems of interdependent and co-evolving units. Even though there is no thermodynamic interpretation, it is still useful to quantify the irreversibility of these systems in terms of stochastic thermodynamics, namely by calculating the entropy production of the whole system as well as for each subsystem and relate it with the topological properties of the underlying network. First, we show the total entropy production increases for the networks with high non-reciprocity of the nodes (i.e., the absolute difference between in-degree and out-degree). The subsystem entropy production also increases with the distance from the reciprocal case (i.e., the same number of in-links and out-links). Finally, we show the validity of the other results of stochastic thermodynamics as speed limit theorems and thermodynamic uncertainty relations.