Complexity in Physics and Chemistry

Complexity is hard to define though rather easy to identify. Statistical mechanics based on nonadditive entropies enables the construction of a clear-cut scenario where nonlinear dynamical and probabilistic ingredients play a crucial role. The main concepts and their experimental validations will be briefly presented. A Bibliography is available at http://tsallis.cat.cbpf.br/biblio.htm

Achieving a transition from the current fossil fuel based economic system to a configuration of green growth is a challenge of global scope. With many heterogeneous entities (individuals, households, companies, institutions, governments, etc.) interacting in networks on multiple levels (e.g., cities, regions, nations), the underlying systems are complex systems. With knowledge and values playing equally important roles in decision making on this subject, stakeholders need to be involved for understanding, as well as addressing this challenge.

We construct an all-inclusive statistical-mechanical model for self-organization based on the hierarchical properties of the nonlinear dynamics towards the attractors that define the period-doubling route to chaos [1-3]. The aforementioned dynamics imprints a sequential assemblage of the model that privileges progressively lower entropies, while a new set of configurations emerges due to the collective partitioning of the original system into secluded portions.

Social influence is among the main driving mechanisms of many collective phenomena in society, including the spreading of innovations, ideas, fads, or social movements. Many of these processes have been modelled either as simple contagion (like the Bass model of innovation diffusion), or as complex contagion (like the Watts model of adoption cascades). In these models social influence is commonly assumed to be homogeneous across ties in the network, while in reality relationships may constitute entirely different dyadic types, modelled as distinct layers in a multiplex network.

Ageing is an ubiquitous mechanism in nature. It has different meanings, depending on the strand of research considered. Classical examples range from non-equilibrium statistical mechanics, where its effects are studied on spin glasses, to biology, considered as the increase of mortality with age of a species, to chemistry, where the properties of a material change over time without any external forces. In any case, ageing can be seen as the dependence of the dynamics of a system on an internal time, often heterogeneously distributed, of the individual components that form such a system.

Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network’s complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis.

The frustration index is a key measure for analysing signed networks, which has been underused due to its computational complexity. We use an exact optimisation-based method to analyse frustration as a global structural property of signed networks coming from diverse application areas. In the classic friend-enemy interpretation of balance theory, a by-product of computing the frustration index is the partitioning of nodes into two internally solidary but mutually hostile groups.

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors.

Individual dispersal propensity is a crucial feature in ecological systems for organisms while searching for a mate or a suitable landscape, foraging, or diminishing the competition. The different ways individuals move is primarily the result of evolution, being survival the ultimate reason for them to disperse. As discussed in [1], dispersal ability can vary within a species as among species.