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As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of…
The theory of natural selection has two forms. Deductive theory describes how populations change over time. One starts with an initial population and some rules for change. From those assumptions, one calculates the future state of the…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
Hierarchical structures are ubiquitous in human and animal societies, but a fundamental understanding of their raison d'\^etre has been lacking. Here, we present a general theory in which hierarchies are obtained as the optimal design that…
We propose a model of the evolution of the networks of scientific citations. The model takes an out-degree distribution (distribution of number of citations) and two parameters as input. The parameters capture the two main ingredients of…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…
Port-Hamiltonian systems theory provides a structured approach to modelling, optimization and control of multiphysical systems. Yet, its relationship to thermodynamics seems to be unclear. The Hamiltonian is traditionally thought of as…
Eukaryote genomes contain excessively introns, inter-genic and other non-genic sequences that appear to have no vital functional role or phenotype manifestation. Their existence, a long-standing puzzle, is viewed from the principle of…
Many mechanisms, functions and structures of life have been unraveled. However, the fundamental driving force that propelled chemical evolution and led to life has remained obscure. The 2nd law of thermodynamics, written as an equation of…
Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…
The purpose of this roadmap article is to draw attention to a paradigm shift in our understanding of evolution towards a perspective of ecological-evolutionary feedback, highlighted through two recent highly simplified examples of rapid…
With the expansion of scientific research, the number of scientific research is increasing. A new urgent problem is raised that how to keep these researches in a proper way. Therefore, knowledge mapping methods come into being, providing a…
Much of the structure in social networks has been explained by two seemingly independent network evolution mechanisms: triadic closure and homophily. While it is common to consider these mechanisms separately or in the frame of a static…
Schr\"odinger bridges have emerged as an enabling framework for unveiling the stochastic dynamics of systems based on marginal observations at different points in time. The terminology "bridge'' refers to a probability law that suitably…
Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…
At any moment in time, evolution is faced with a formidable challenge: refining the already highly optimised design of biological species, a feat accomplished through all preceding generations. In such a scenario, the impact of random…
Partial orders have been used to model several experimental setups, going from classical thermodynamics and general relativity to the quantum realm with its resource theories. In order to study such experimental setups, one typically…
Modern materials science has historically been founded on combining restricted subsets of the periodic table, favoring high-purity, few-element systems. However, the demands of an emerging circular economy, together with the need to…
Darwinian dynamics is manifestly stochastic and nonconservative, but has a profound connection to conservative dynamics in physics. In the present paper the main ideas and logical steps leading to thermodynamics from Darwinian dynamics are…