Abstract

Predicting the behaviour of many-body systems at large scales of space and time is one of the most important problems of emergent physics. Hydrodynamics provides a powerful framework, which allows us to describe in a universal fashion macroscopic motion and fluctuations on top of it. I will discuss the general form of the hydrodynamic equations, how it is constrained by principles of statistical mechanics, and how it gives access to large-scale fluctuations and correlations. I will explain how “PT symmetry” guarantees entropy production and irreversibility of the hydrodynamic equation, and I will introduce the ``ballistic macroscopic fluctuation theory” (BMFT), which predicts that long-range spatial correlations develop over time if the initial state of the many-body system is spatially inhomogeneous. This is based on works with J. De Nardis, and with G. Perfetto, T. Sasamoto and T. Yoshimura.