The physics of spreading ideas

Here we show that the main features of citations history (S-shaped curve, increasing h index, decreasing m quotient) are predictable with the constructal law of how an idea flows over a populated territory. It flows in two ways: fast and long, as “convection” along established channels of researchers interested in the idea, and slow and short, sideways from channels, by “diffusion” to new users. The first regime accounts for the rising portion of the S curve, and the second for the slow-down. Tree-shaped established channels spread the idea faster than single channels over the same area. The complexity of the design of fast channels increases in time due to the evolution of communications technologies.