The quantum q-divergence is the nonadditive relative entropy associated with the Tsallis entropy indexed by q. Here, its basic properties including the q-deformation and quantum-group structure, convexity and monotonicity are summarized. Then, it is applied to measuring the degree of state...

A statistical measure of complexity utilising the concept of entropy or information is proposed. Our way in this study is to use a nonextensive entropy instead of an extensive (additive) Shannon entropy in the definition, but can be characterised as a difference between the qth-order Rényi...

The paper elaborates an endeavor on applying the algorithmic information-theoretic computational complexity to meta-social-sciences. It is motivated by the effort on seeking the impact of the well-known incompleteness theorem to the scientific methodology approaching social phenomena. The paper...

Non-extensive thermostatistics is a new paradigm statistical mechanics (SM) that has reached the rather mature age of 15 in 2003. It has considerably extended both SM formalism and its range of applicability. It constitutes one of physics’ new frontiers, with advances being made almost on a...

It is well known that transition rates in a canonical ensemble should respect the principle of detailed balance. What are the equivalent constraints that apply in non-equilibrium steady states, implied by maximization of information-entropy? The exact theorem for the non-equilibrium rates yields...

The unprecedented access offered by the World Wide Web brings with it the potential to gather huge amounts of data on human activities. Here we exploit this by using a toy model of financial markets, the Minority Game (MG), to investigate human speculative trading behaviour and information...