Diffusion of innovations dynamics, biological growth and catenary function

• We propose an entropic connection between the catenary function and the aggregate logistic model.
• We find a linkage between logistic and Bass models for diffusion of innovations in social systems.
• Generalized Bass models determine perturbed catenaries through a control function.
• These entropic correspondences suggest a physical connection between static and dynamic equilibria.
• This invariance may be motivated by the Verlinde’s conjecture on the entropic origin of gravity.

The catenary function has a well-known role in determining the shape of chains and cables supported at their ends under the force of gravity. This enables design using a specific static equilibrium over space. Its reflected version, the catenary arch, allows the construction of bridges and arches exploiting the dual equilibrium property under uniform compression. In this paper, we emphasize a further connection with well-known aggregate biological growth models over time and the related diffusion of innovation key paradigms (e.g., logistic and Bass distributions over time) that determine self-sustaining evolutionary growth dynamics in naturalistic and socio-economic contexts. Moreover, we prove that the ‘local entropy function’, related to a logistic distribution, is a catenary and vice versa. This special invariance may be explained, at a deeper level, through the Verlinde’s conjecture on the origin of gravity as an effect of the entropic force.