Angelo Vulpiani
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…
We present a non-perturbative, mean-field theory for the Fermi-Pasta-Ulam-Tsingou model with quartic interaction, capturing the quasiperiodic features shown by the system at all energies in the thermodynamic limit. Starting from the true…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
Current research in statistical mechanics mostly concerns the investigation of out-of-equilibrium, irreversible processes, which are ubiquitous in nature and still far from being theoretically understood. Even the precise characterization…
Random exchange kinetic models are widely employed to describe the conservative dynamics of large interacting systems. Due to their simplicity and generality, they are quite popular in several fields, from statistical mechanics to…
When analyzing the equilibrium properties of a stochastic process, identifying the parity of the variables under time-reversal is imperative. This initial step is required to assess the presence of detailed balance, and to compute the…
In this paper we present a discussion of the basic aspects of the well-known problem of prediction and inference in physics, with specific attention to the role of models, the use of data and the application of recent developments in…
The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here…
We consider the Prandtl-Tomlinson model in the case of a constant driving force and in the presence of thermal fluctuations. We show that the system dynamics is well reproduced by a simplified description obtained through a Markov process,…
The characterization of the distance from equilibrium is a debated problem in particular in the treatment of experimental signals. If the signal is a 1-dimensional time-series, such a goal becomes challenging. A paradigmatic example is the…
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…
In this paper, we offer to the reader an essential review of the theory of Fluctuation-Dissipation Relations (FDR), from the first formulations due to Einstein and Onsager, to the recent developments in the framework of stochastic…
The detection of cause-effect relationships from the analysis of paleoclimatic records is a crucial step to disentangle the main mechanisms at work in the climate system. Here, we show that the approach based on the generalized…
Recent numerical results showed that thermalization of Fourier modes is achieved in short time-scales in the Toda model, despite its integrability and the absence of chaos. Here we provide numerical evidence that the scenario according to…
We study the anomalous transport in systems of random walks (RW's) on comb-like lattices with fractal sidebranches, showing subdiffusion, and in a system of Brownian particles driven by a random shear along the x-direction, showing a…
We introduce a general formulation of the fluctuation-dissipation relations (FDR) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require the explicit knowledge of…
We investigate the effect of coarse-graining on the energetics properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a…