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Data from experiments and theoretical arguments are the two pillars sustaining the job of modelling physical systems through inference. In order to solve the inference problem, the data should satisfy certain conditions that depend also upon the particular questions addressed in a research. Here we focus on the characterization of systems in terms of a distance from equilibrium, typically the entropy production (time-reversal asymmetry) or the violation of the Kubo fluctuation-dissipation relation. We show how general, counter-intuitive and negative for inference, is the problem of the impossibility to estimate the distance from equilibrium using a series of scalar data which have a Gaussian statistics. This impossibility occurs also when the data are correlated in time, and that is the most interesting case because it usually stems from a multi-dimensional linear Markovian system where there are many time-scales associated to different variables and, possibly, thermal baths. Observing a single variable (or a linear combination of variables) results in a one-dimensional process which is always indistinguishable from an equilibrium one (unless a perturbation-response experiment is available). In a setting where only data analysis (and not new experiments) is allowed, we propose - as a way out - the combined use of different series of data acquired with different parameters. This strategy works when there is a sufficient knowledge of the connection between experimental parameters and model parameters. We also briefly discuss how such results emerge, similarly, in the context of Markov chains within certain coarse-graining schemes. Our conclusion is that the distance from equilibrium is related to quite a fine knowledge of the full phase space, and therefore typically hard to approximate in real experiments., Comment: 23 pages - 8 figures

The way granular materials response to an applied shear stress is of the utmost relevance to both human activities and natural environment. One of the their most intriguing and less understood behavior, is the stick-instability, whose most dramatic manifestation are earthquakes, ultimately governed by the dynamics of rocks and debris jammed within the fault gauge. Many of the features of earthquakes, i.e. intermittency, broad times and energy scale involved, are mimicked by a very simple experimental set-up, where small beads of glass under load are slowly sheared by an elastic medium. Analyzing data from long lasting experiments, we identify a critical dynamical regime, that can be related to known theoretical models used for "crackling-noise" phenomena. In particular, we focus on the average shape of the slip velocity, observing a "breakdown of scaling": while small slips show a self-similar shape, large does not, in a way that suggests the presence of subtle inertial effects within the granular system. In order to characterise the crossover between the two regimes, we investigate the frictional response of the system, which we trat as a stochastic quantity. Computing different averages, we evidence a weakening effect, whose Stribeck threshold velocity can be related to the aforementioned breaking of scaling., 11 pages, 14 figures

We discuss various situations where the formation of rocky coast morphology can be attributed to the retro-action of the coast morphology itself on the erosive power of the sea. Destroying the weaker elements of the coast, erosion can creates irregular seashores. In turn, the geometrical irregularity participates in the damping of sea-waves, decreasing their erosive power. There may then exist a mutual self-stabilization of the wave amplitude together with the irregular morphology of the coast. A simple model of this type of stabilization is discussed. The resulting coastline morphologies are diverse, depending mainly on the morphology/damping coupling. In the limit case of weak coupling, the process spontaneously builds fractal morphologies with a dimension close to 4/3. This provides a direct connection between the coastal erosion problem and the theory of percolation. For strong coupling, rugged but non-fractal coasts may emerge during the erosion process, and we investigate a geometrical characterization in these cases. The model is minimal, but can be extended to take into account heterogeneity in the rock lithology and various initial conditions. This allows to mimic coastline complexity, well beyond simple fractality. Our results suggest that the irregular morphology of coastlines as well as the stochastic nature of erosion are deeply connected with the critical aspects of percolation phenomena., Comment: 34 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:cond-mat/0311509

We analyze a large-scale snapshot of del.icio.us and investigate how the number of different tags in the system grows as a function of a suitably defined notion of time. We study the temporal evolution of the global vocabulary size, i.e. the number of distinct tags in the entire system, as well as the evolution of local vocabularies, that is the growth of the number of distinct tags used in the context of a given resource or user. In both cases, we find power-law behaviors with exponents smaller than one. Surprisingly, the observed growth behaviors are remarkably regular throughout the entire history of the system and across very different resources being bookmarked. Similar sub-linear laws of growth have been observed in written text, and this qualitative universality calls for an explanation and points in the direction of non-trivial cognitive processes in the complex interaction patterns characterizing collaborative tagging., Comment: 6 pages, 7 figures

We study the formation and the dynamics of correlations in the velocity field for 1D and 2D cooling granular gases with the assumption of negligible density fluctuations (``Homogeneous Velocity-correlated Cooling State'', HVCS). It is shown that the predictions of mean field models fail when velocity fluctuations become important. The study of correlations is done by means of molecular dynamics and introducing an Inelastic Lattice Maxwell Models. This lattice model is able to reproduce all the properties of the Homogeneous Cooling State and several features of the HVCS. Moreover it allows very precise measurements of structure functions and other crucial statistical indicators. The study suggests that both the 1D and the 2D dynamics of the velocity field are compatible with a diffusive dynamics at large scale with a more complex behavior at small scale. In 2D the issue of scale separation, which is of interest in the context of kinetic theories, is addressed., 24 pages, 16 figures, conference proceeding

We present a numerical study of the non-equilibrium dynamics of the Sherrington-Kirkpatrick model. We analize the overlap distribution between the configurations visited at the time t and in particular its scaling behaviour with the size of the system. We find two different non-equilibrium dynamical regimes. The first is a proper Out of Equilibrium Regime, that is the relevant regime for the dynamics of an infinite system. The second is an Intermediate Regime that separates the Out of Equilibrium Regime from equilibrium. After studying the crossover beetween the two regimes, we focus on the Out of Equilibrium Regime and we reveal some of the geometrical features of phase space. According to recent analitical work, we find that the asymptotic out of equilibrium energy density is the equilibrium one. The same happens to the staggered-magnetisation, suggesting there is a deep geometrical similarity between equilibrium and out of equilibrium configurations. A procedure, that we call clonation, shows that the dynamics follows sort of canyons, as opposed to a system of independent traps., 20 pages, LaTeX2e, 11 figures, epsf.sty. Also available at ftp://hpteo.roma1.infn.it/pub/preprints/andreab/sk-offeq.tar.gz

We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular media. Thereafter, dilute systems, the so-called "granular gases" are discussed: idealized kinetic models, such as the gas of inelastic hard spheres in the cooling regime, are the optimal playground to study the slow growth of correlated structures, e.g. shear patterns, vortices and clusters. In fluidized experiments, liquid-gas or solid-gas separations have been observed. In the case of monolayers of particles, phase coexistence and coarsening appear in several different setups, with mechanical or electrostatic energy input. Phenomenological models describe, even quantitatively, several experimental measures, both for the coarsening dynamics and for the dynamic transition between different granular phases. The origin of the underlying bistability is in general related to negative compressibility from granular hydrodynamics computations, even if the understanding of the mechanism is far from complete. A relevant problem, with important industrial applications, is related to the demixing or segregation of mixtures, for instance in rotating tumblers or on horizontally vibrated plates. Finally, the problem of compaction of highly dense granular materials, which has many important applications, is usually described in terms of coarsening dynamics: there, bubbles of mis-aligned grains evaporate, allowing the coalescence of optimally arranged islands and a progressive reduction of total occupied volume., Comment: 12 pages, 10 figures, to appear in "Dynamics of coarsening" Comptes Rendus Physique special issue, https://sites.google.com/site/ppoliti/crp-special-issue