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