Entropy production and fluctuation theorems on complex networks.

Entropy production (EP) is a fundamental quantity useful for understanding irreversible process. In stochastic thermodynamics, EP is more evident in probability density functions of trajectories of a particle in the state space. Here, inspired by a previous result that complex networks can serve as state spaces, we consider a data packet transport problem on complex networks. EP is generated owing to the complexity of pathways as the packet travels back and forth between two nodes along the same pathway. The total EPs are exactly enumerated along all possible shortest paths between every pair of nodes, and the functional form of the EP distribution is proposed based on our numerical results. We confirm that the EP distribution satisfies the detailed and integral fluctuation theorems. Our results should be pedagogically helpful for understanding trajectory-dependent EP in stochastic processes and exploring nonequilibrium fluctuations associated with the entanglement of dividing and merging among the shortest pathways in complex networks.