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Description
One of the foundations of statistical physics is that only minimal information is required for the description of macroscopic systems.
Research in quantum one-dimensional integrable systems out of equilibrium has recently revealed relaxation towards a non-thermal
statistical ensemble that violates this principle due to the presence of an infinite number of local integrals of motion. The information
content of this ensemble remains however a riddle. By studying the dynamics after suddenly switching-off the interactions in an isolated
quantum system (a so-called quantum quench), we will show that the time evolution under a massive Gaussian field theory erases all memory
of non-Gaussian correlations that are present in the initial state, keeping information only about the initial two-point correlation
function. In the massless case on the other hand, we will show that an enormous amount of information about the initial state survives
even at infinitely large times, in contrast to earlier expectations. We provide an intuitive explanation of the above results based on the
cluster decomposition principle and the hydrodynamic character of the evolution. Lastly we will discuss applications to cold atom
experiments and generalisations to lattice systems and spin chains as well as conformal field theories.
