In the last decades, statistical mechanics pushed its frontiers to encompass systems which fall outside the standard equilibrium framework. Paradigmatic examples are non-equilibrium systems such as granular and active matter for which, either due to dissipative interactions or as a consequence of "self-driven motility", even basic thermodynamic quantities, such as temperature and pressure, are not well defined. Systems with long-range interactions, like gravitational or Coulomb ones, are another example where the standard equilibrium picture is not appropriate. Systems with local interactions can also display slow relaxation, for example because a critical point exists between the initial state and the equilibrium state or as an effect of the existence of more than one conservation law. Quandaries are also present for transport properties because of the lack of a suitable coarse-grained description able to manage the complexity of the phenomenon. This necessity emerges in the context of granular materials, or in the presence of the interplay between self-motility and advection by an external flow as well as in problems of diffusion in highly confining geometries or complex topologies. A related issue is that of the validity of generalised fluctuation-dissipation relations, in particular in non-linear regimes.
Standard tools for the derivation of generalized thermodynamics and transport equations are valid for a Hamiltonian dynamics with short-range interactions, large number of degrees of freedom and negligible effects of the boundaries. In all the above-mentioned examples, at least one of these conditions is not fulfilled. Although these systems can be quite different, they share certain similar features, such as large non-Gaussian fluctuations, non-equilibrium currents, complex spatio-temporal patterns, suggesting the possibility of a common theoretical framework.
In this project, we will build upon our competences in statistical mechanics, stochastic processes and dynamical systems. Our challenge is to use a clever combination of empirical laws, hints from simplified models and numerical simulations as well as experiments in granular media, with the ambition to develop a consistent description of generalized thermodynamics and transport properties of systems lacking a standard equilibrium reference state.
Besides the progress in the comprehension of fundamental mechanisms, the approaches that we will develop within this project are expected to contribute to refine advanced technologies: for example, improving hydrodynamic modelling of granular matter would be key to the industrial optimization of powder transport; achieving a good control of bio-polymer transport would boost the performance on biosensors devices; understanding the interplay of self-propulsion and passive advection would improve the efficiency of bioreactors for industrial growth of motile microorganisms; the study of anomalous transport is relevant for optimising the conductive properties of electronic nanodevices.