Universal Equation for Non Equilibrium Correlations in Interacting Particle Systems

An open system out of equilibrium exchanges matter, energy, or information with its surroundings through directed currents that break time-reversal symmetry. Far from equilibrium, the arrow of time becomes crucial. While equilibrium physics is well explained by statistical physics, understanding non-equilibrium systems is a major challenge in modern physics. Do universal laws exist far from equilibrium? How can complex systems’ dynamics be characterized?Interacting particle systems (IPS), driven by external fields or prepared with an initial inhomogeneous density profile, are the “hydrogen atom” of non-equilibrium physics. Very recently, we have made important progress for the Symmetric Exclusion Process (SEP), a paradigmatic model of one-dimensional IPS, and showed by relying on a novel approach that this many-body dynamics in fact reduces to a simple single-body exact closed equation for the correlations, which can be solved explicitly. Beyond the particular case of the SEP, this striking but puzzling result changes our views and opens new horizons in the analysis of IPS by reducing them to single-body problems. Unveiling the corresponding universal closed equation for correlations in general IPS, along with the underlying theoretical framework of non-equilibrium statistical physics, is the objective of this project. The achievability of this challenging task is supported by promising recent developments both for diffusive systems (which obey Fick’s law) and for ballistic systems. These results will provide explicit characterization of transport properties in general IPS, conceptually new tools to analyse interacting particle systems and finally resolve the long-standing challenge of formulating a general framework for non-equilibrium statistical physics.