We describe, in a short overview, the construction of a Nonequilibrium Statistical Mechanics Ensemble Formalism, providing a thermo-statistical theory of kinetic and relaxation processes. Such construction has been approached along the recently past 20th century by a pleiad of distinguished scientists, a work that can be subsumed in a large systematization in the form of a physically sound, general and useful, theoretical framework. We briefly comment on the main questions associated to that construction. Among them are the relevant ones of choice of the basic variables, and of historicity and irreversibility. The derivation of a nonequilibrium grand-canonical statistical operator and a brief description of the all-important accompanying Nonlinear Quantum Kinetic Theory of relaxation processes are presented. The aspect of validation of the theory (comparison of theory and experiment) is reviewed in compact form, and its use is illustrated in a study of a nonequilibrium system of quantum oscillators embedded in a thermal bath and under the action of an external force, showing how a far-reaching generalization of Mori–Langevin equations arises.

We present an analysis of the emergence of a nonequilibrium Bose-Einstein-type condensation of magnons in radio-frequency pumped magnetic thin films, which has recently been experimentally observed. A complete description of all the nonequilibrium processes involved is given. It is demonstrated that the phenomenon is another example of the emergence of Bose-Einstein-type condensation in nonequilibrium many-boson systems embedded in a thermal bath, a phenomenon evidenced decades ago by the renowned late Herbert Fröhlich.with q running over the Brillouin zone. The single-magnon density matrix is composed of the diagonal elements N q = c q † c q ͑called populations͒ and the nondiagonal ones N q,Q = c q+Q/2 † c q−Q/2 with Q 0. The latter, describing the local inhomogeneities of the populations N q , are not relevant for the present problem once space-resolved experiments are PHYSICAL REVIEW B 82, 140404͑R͒ ͑2010͒

Abstract. The emergence of a non-equilibrium Bose-Einstein-like condensation of magnons in rf-pumped magnetic thin films has recently been experimentally observed. We present here a complete theoretical description of the non-equilibrium processes involved. It it demonstrated that the phenomenon is another example of the presence of a Bose-Einstein-like condensation in nonequilibrium many-boson systems embedded in a thermal bath, better referred-to as Fröhlich-Bose-Einstein condensation. The complex behavior emerges after a threshold of the exciting intensity is attained. It is inhibited at higher intensities when the magnon-magnon interaction drives the magnons to internal thermalization. The observed behavior of the relaxation to equilibrium after the end of the pumping pulse is also accounted for and the different processes fully described.

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We consider the case of a peculiar complex behavior in open boson systems sufficiently away from equilibrium, having relevance in the functioning of information-processing biological and condensed matter systems. This is the so-called Fröhlich–Bose–Einstein condensation, a self-organizing-synergetic dissipative structure, a phenomenon apparently working in biological processes and present in several cases of systems of boson-like quasi-particles in condensed inorganic matter. Emphasis is centered on the quantum-mechanical-statistical irreversible thermodynamics of these open systems, and the informational characteristics of the phenomena

This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.

We explore the dynamics of an epidemiological disease spreading within a complex network of individuals. The local behavior of the epidemics is modelled by means of an excitable dynamics, and the individuals are connected in the network through a weighted small-world wiring. The global behavior of the epidemics can have stationary as well as chaotic states, depending upon the probability of substituting short-range with long-range interactions. We describe the bifurcation scenario leading to such latter states, and discuss the relevance of the observed chaotic dynamics for the description of the spreading mechanisms of epidemics inside complex networks.

The Sznajd model (SM) has been employed with success in the last years to describe opinion propagation in a community. In particular, it has been claimed that its transient is able to reproduce some scale properties observed in data of proportional elections, in different countries, if the community structure (the network) is scale-free. In this work, we investigate the properties of the transient of a particular version of the SM, introduced by Bernardes and co-authors in 2002. We studied the behavior of the model in networks of different topologies through the time evolution of an order parameter known as interface density, and concluded that regular lattices with high dimensionality also leads to a power-law distribution of the number of candidates with v votes. Also, we show that the particular absorbing state achieved in the stationary state (or else, the winner candidate), is related to a particular feature of the model, that may not be realistic in all situations.