  This work demonstrates the application of a birth-death Markov process,
inspired by radioactive decay, to capture the dynamics of innovation processes.
Leveraging the Bass diffusion model, we derive a Gompertz-like function
explaining the long-term innovation trends. The validity of our model is
confirmed using citation data, Google trends, and a recurrent neural network,
which also reveals short-term fluctuations. Further analysis through an
automaton model suggests these fluctuations can arise from the inherent
stochastic nature of the underlying physics.
