This paper offers novel insights regarding the role of complexity in both the transitional and the long-run dynamics of the economy. We devise an endogenous growth model using the concept of entropy as a state-dependent complexity effect. This allows us to gradually diminish scale effects as the economy develops along the transitional dynamics, which conciliates evidence on the existence of scale effects in history with evidence of no or reduced scale effects in today’s economies. We show that empirical evidence supports entropy as a “first principle” operator of the complexity effect. The model features endogenous growth, with null or small (positive or negative) scale effects, or stagnation, in the long run. These different long-run possibilities have also policy implications. Then, we show that the model can replicate well the take-off after the industrial revolution and the productivity slowdown in the second half of the XXth century. Future scenarios based on in-sample calibration are discussed, and may help to explain (part of) the growth crises affecting the current generation.