Abstract: Relativistic hydrodynamics plays a pivotal role in understanding some of the most extreme environments in the universe. These include the quark-gluon plasma formed in high-energy nuclear collisions or neutron star merges. The key organizational principle underlying relativistic hydrodynamics is the gradient expansion, a perturbative scheme where the leading order term represents ideal fluid flows - which do not produce entropy - while the remaining higher-order ones capture dissipation.
Until recently, our understanding of the large-order behavior of this gradient expansion has been restricted to two limiting scenarios: generic fluid flows in the linear response regime and nonlinear comoving flows highly constrained by symmetries. In this talk, I will first provide new evidence demonstrating that, at the nonlinear level, the gradient expansion is a factorially divergent series beyond comoving flows. Then, I will discuss how singulants offer a new perspective to understand the asymptotic behavior of the gradient expansion in general situations. Singulants emerge from a dramatic reorganization of the gradient expansion at large orders. I will show that they obey simple equations of motion dictated by linear response around the local state of the fluid and provide explicit examples where they rule the optimal truncation of the gradient expansion.