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This paper mainly discusses the diffusion on complex networks withtime-varying couplings. We propose a model to describe the adaptive diffusionprocess of local topological and dynamical information, and find that theBarabasi-Albert scale-free network (BA network) is beneficial to the diffusionand leads nodes to arrive at a larger state value than other networks do. Theability of diffusion for a node is related to its own degree. Specifically,nodes with smaller degrees are more likely to change their states and reachlarger values, while those with larger degrees tend to stick to their originalstates. We introduce state entropy to analyze the thermodynamic mechanism ofthe diffusion process, and interestingly find that this kind of diffusionprocess is a minimization process of state entropy. We use the inequalityconstrained optimization method to reveal the restriction function of theminimization and find that it has the same form as the Gibbs free energy. Thethermodynamical concept allows us to understand dynamical processes on complexnetworks from a brand-new perspective. The result provides a convenient meansof optimizing relevant dynamical processes on practical circuits as well asrelated complex systems.

Adaptive Diffusion Processes of Time-Varying Local Information on Networks