Andrea Baldassarri

CNR - Istituto dei Sistemi Complessi, Roma

Asymmetric fluctuation shapes

Since the Einstein's historical work on Brownian motion, fluctuations have become an important source of investigation in physics. Nowadays, we know that fluctuations are not a mere annoying disturbance in the measure of average quantities, but they can be leveraged to provide insightful physical information, as in the case of phase transitions,  where specific quantities (critical exponents) allowed to identify unsuspected similarities between very different systems. 

In this talk, we consider a different measure which could help in characterizing and discriminating different kind of fluctuations: the average shape of a fluctuation. It can be generally defined as the average temporal evolution that a signal experiences when it deviates from a reference value (for instance, but not limited to, its stationary average) during a fixed time interval.

This quantity has first been introduced in the context of ferromagnetism, where the fluctuations in study come from electrical signals during hysteresis cycles of a ferromagnetic material. The phenomenology, first observed by Barkhausen, was then named "crackling-noise" because of its intermittent, bursting nature, and it has been advocated as a paradigm relevant for many different and diverse systems, from earthquakes to plastic deformation of materials, from astrophysics to the dynamics of granular matter. The simplest stochastic model for this phenomena is the ABBM model, proposed in the eighty by a group of Italian researchers, led by Bertotti. The model predicts a specific, symmetric scaling form for the average fluctuation shapes of different durations, that can be computed analytically and which agrees most of the time with the experimental observations.

A laboratory experiment on friction in granular media, set up by Alberto Petri and collaborators, produces a cracking signal reminiscent of seismic activity and Barkhausen noise, and it represents a perfect playground for these studies. Nevertheless, recent measures for the average shape of fluctuations in this experiments evidence a breaking of the scaling predicted by the ABBM model, when the average fluctuation shape becomes asymmetric.

In order to investigate the meaning of such asymmetry, which implies a broken time reversal symmetry in the dynamics, we considered an extension of the ABBM model, which is also related to the very first model proposed by Einstein: the Brownian Gyrator. This model has been recently taken into account in the context of stochastic thermodynamics, as the simplest example of a non-equilibrium system characterized by thermal inhomogeneities: it is the simplest possible model describing a system in simultaneous contact with two different thermal sources.

We present a systematic study of the average shapes of fluctuations of the Brownian Gyrator. They show surprising analogies with the phenomenology observed in the granular friction experiment, suggesting how the shape asymmetry can be used as a probe for the energy production of non-equilibrium systems.