Emergent symmetries of relativistic fluid dynamics from local ergodicity

TL;DR

This paper demonstrates that certain symmetries in relativistic fluid dynamics emerge from local ergodicity assumptions, providing a new perspective on deriving ideal hydrodynamics in complex, fluctuating systems.

Contribution

It introduces a novel approach to deriving relativistic ideal fluid symmetries from local ergodicity, linking microscopic assumptions to macroscopic fluid behavior.

Findings

Symmetries emerge from local ergodicity assumptions.

Connection established between ergodicity and ideal hydrodynamics.

Insights into thermalization and deviations in small systems.

Abstract

We show that volume-preserving diffomorphisms and the chemical shift symmetry defining relativistic lagrangian ideal fluid dynamics can be derived as an emerging symmetry when ergodicity is assumed to apply locally in a way that is invariant under smooth spacetime foliations. This can be used as a way to derive the ideal hydrodynamic limit in a strongly coupled but strongly fluctuating medium. We comment on the connection with thermalization in small systems, the Eigenstate thermalization hypothesis and deviations from the ideal limit.