Theory of Entropy Production
Entropy Product (EP) is a pivotal quantity useful for understanding irretrievable process. In stochastic thermodynamics, EP is more putative in probability viscidity functions of circuits of a patch in the state space. Presently, inspired by a precedent 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 nodules along the same pathway. The total EPs are exactly enumerated along all possible shortest paths between every dyad of nodules, and the functional form of the EP distribution is proposed predicated on our numerical results. We confirm that the EP distribution satisfies the detailed and integral inconstancy theorems. The results should be pedagogically helpful for understanding circuit-dependent EP in stochastic processes and exploring nonequilibrium inconstancies associated with the web of dividing and integrating among the shortest pathways in complex networks.
Joseph Spakowitz (USA)