Physical modelling of global macrosystems evolution

The recently introduced Theory of the Adjacent Possible (TAP) is a model of combinatorial innovation aiming to explain the "hockey-stick" upward trend of human technological evolution, where an explosion in the number of produced items with increasing complexity suddenly occurs. In addition, the TAP model was also used to explain the rapidly emerging biological complexity. Inspired by TAP here we propose a reaction-diffusion system aiming to extend the model in both space and...

We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increas...

Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical thermodynamics. In particular we can demonstrate the existence of several distinct phases of evolutionary dynamics: a phase of fast growing diversity, one of stationary, finite diversity, and one of rapidly decaying diversity. While the first two pha...

It has been suggested that innovations occur mainly by combination: the more inventions accumulate, the higher the probability that new inventions are obtained from previous designs. Additionally, it has been conjectured that the combinatorial nature of innovations naturally leads to a singularity: at some finite time, the number of innovations should diverge. Although these ideas are certainly appealing, no general models have been yet developed to test the conditions under ...

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker. The presence of the network naturally accounts for the mechanism of the adjacent possible, and the model r...

We provide a theoretical framework to understand when firms may benefit from exploiting previously abandoned technologies and brands. We model for the long run process of innovation, allowing for sustainable diversity and comebacks of old brands and technologies. We present two extensions to the logistic and Lotka-Volterra equations, which describe the diffusion of an innovation. First, we extend the short-term competition to a long-term process characterized by a sequence of...

In this work, we introduce an extremely general model for a collection of innovation processes in order to model and analyze the interaction among them. We provide theoretical results, analytically proven, and we show how the proposed model fits the behaviors observed in some real data sets (from Reddit and Gutenberg). It is worth mentioning that the given applications are only examples of the potentialities of the proposed model and related results: due to its abstractness a...

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 fl...

The notion of the "adjacent possible" has been advanced to theorize the generation of novelty across many different research domains. This study is an attempt to examine in what way the notion can be made empirically useful for innovation studies. A theoretical framework is construed based on the notion of innovation a search process of recombining knowledge to discover the "adjacent possible". The framework makes testable predictions about the rate of innovation, the distrib...

Innovation and its complement exnovation describe the progression of realized possibilities from the past to the future, and the process depends on the structure of the underlying graph. For example, the phylogenetic tree represents the unique path of mutations to a single species. To a technology, paths are manifold, like a "truss." We solve for the phase diagram of a model, where a population innovates while outrunning exnovation. The dynamics progress on random graphs that...