Abstract:
In this paper we discuss the nonergodic behavior for a class of long-standing quasi-stationary states in a paradigmatic model of long-range interacting systems, i.e. the HMF model. We show that ensemble averages and time averages for velocities probability density functions (pdfs) do not coincide and in particular the latter exhibit a tendency to converge towards a q-Gaussian attractor instead of the usual Gaussian one predicted by the Central Limit Theorem, when ergodicity applies.

Abstract:
The Hamiltonian Mean Field model describes a system of N fully-coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the critical point. In particular, when the particles are prepared in a ``water bag'' initial state, the relaxation to equilibrium is very slow. In the transient time the system lives in a dynamical quasi-stationary state and exhibits anomalous (enhanced) diffusion and L\'evy walks. In this paper we study temperature and velocity distribution of the quasi-stationary state and we show that the lifetime of such a state increases with N. In particular when the $N\to \infty$ limit is taken before the $t \to \infty$ limit, the results obtained are different from the expected canonical predictions. This scenario seems to confirm a recent conjecture proposed by C.Tsallis.

Abstract:
An instructive and apparently simple model of fully-coupled rotators, the so-called Hamiltonian Mean Field (HMF) model, together with a generalized version with variable interaction range, have revealed a very complex out-of-equilibrium dynamics which can be considered paradigmatic for nonextensive systems. In this short paper we illustrate the interesting anomalous pre-equilibrium dynamics, focusing on the novel connections to the generalized nonextensive thermostatistics and the recent links to glassy systems.

Abstract:
We present an analysis of a time series of a wind strength measurements recorded at Florence airport in the period October 2002 - March 2003. The data were taken simultaneously by two runway head anemometers, located at a distance of 900 m, at a frequency of 3.3 10-3 Hz. The data show strong correlations over long time spans over a few tens of hours. We performed an analysis of wind velocity as it is usually done for turbulence laboratory experiments. Wind velocity returns and wind velocity differences were considered. The pdfs of these quantities exhibit strong non-Gaussian fat tails. The distribution of the standand deviations of the fluctuations can be successfully reproduced by a Gamma distribution, while the Log-normal one fails completely. Following Beck and Cohen superstatistics approach, we extract the Tsallis entropic index q from this Gamma distribution. The corresponding q-exponential curves reproduce with a very good accuracy the pdfs of returns and velocity differences.

Abstract:
We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian Mean Field model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi stationary states observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable states in the Kuramoto model and discuss the similarities with those found in the HMF model. The existence of metastability seem to be quite a common phenomenon in fully coupled systems, whose origin could be also interpreted as a dynamical mechanism preventing or hindering sinchronization.

Abstract:
We review the anomalies of the HMF model and discuss the robusteness of the glassy features vs the initial conditions. Connections to Tsallis statistics are also addressed.

Abstract:
In the comment by T.Dauxois et al.,(cond-mat/0605445), the authors question our application of the nonextensive statistical mechanics proposed by Tsallis, to explain the anomalous dynamics of the Hamiltonian Mean Field (HMF) model. More specifically they claim that the explanation of the metastability found in the out-of-equilibrium dynamics is only a fitting procedure and is also in contrast with a previous application. This criticism mostly relies on recent studies based on the Vlasov approach, where the authors claim to explain the anomalous behaviour of the HMF model in terms of a standard formalism. In order to reply to this comment we want to stress a few numerical facts and conclude with some final considerations. A recent paper by P-H. Chavanis (cond-mat/0604234) is also important to clarify the question here debated.

Abstract:
We successfully apply the recent developed superstatistics theory to a temporal series of turbulent wind measurements recorded by the anemometers of Florence airport. Within this approach we can reproduce very well the fluctuations and the pdfs of wind velocity returns and differences.

Abstract:
In the late sixties the Canadian psychologist Laurence J. Peter advanced an apparently paradoxical principle, named since then after him, which can be summarized as follows: {\it 'Every new member in a hierarchical organization climbs the hierarchy until he/she reaches his/her level of maximum incompetence'}. Despite its apparent unreasonableness, such a principle would realistically act in any organization where the mechanism of promotion rewards the best members and where the mechanism at their new level in the hierarchical structure does not depend on the competence they had at the previous level, usually because the tasks of the levels are very different to each other. Here we show, by means of agent based simulations, that if the latter two features actually hold in a given model of an organization with a hierarchical structure, then not only is the Peter principle unavoidable, but also it yields in turn a significant reduction of the global efficiency of the organization. Within a game theory-like approach, we explore different promotion strategies and we find, counterintuitively, that in order to avoid such an effect the best ways for improving the efficiency of a given organization are either to promote each time an agent at random or to promote randomly the best and the worst members in terms of competence.

Abstract:
We discuss two models of opinion dynamics. First wepresent a brief review of the Hegselmann and Krause (HK) compromise model in two dimensions, showing that it is possible to simulate the dynamics in the limit of an infinite number of agents by solving numerically a rate equation for a continuum distribution of opinions. Then, we discuss the Opinion Changing Rate (OCR) model, which allows to study under which conditions a group of agents with a different natural tendency (rate) to change opinion can find the agreement. In the context of the this model, consensus is viewed as a synchronization process.