Perfect Fluids

TL;DR

This paper introduces a generalized theory of perfect fluids that incorporates new variables and symmetries, leading to observable corrections in fluid dynamics and new insights into the behavior of scale-invariant fluids.

Contribution

The authors develop a novel framework for perfect fluids without boost symmetry, including a new kinetic mass density variable and extending the theory to scale-invariant fluids with arbitrary critical exponent z.

Findings

Derived corrections to Euler equations that could be experimentally observed.

Provided new expressions for the speed of sound in perfect fluids.

Analyzed thermodynamics and fluid behavior of Lifshitz particles and gases.

Abstract

We develop a new theory of perfect fluids with translation and rotation symmetry, which is also applicable in the absence of any type of boost symmetry. It involves introducing a new fluid variable, the kinetic mass density, which is needed to define the most general energy-momentum tensor for perfect fluids. Our theory leads to corrections to the Euler equations for perfect fluids that might be observable in hydrodynamic fluid experiments. We also derive new expressions for the speed of sound in perfect fluids. Our theory reduces to the known perfect fluid models when boost symmetry is present. It can also be adapted to (non-relativistic) scale invariant fluids with critical exponent $z$. We show that perfect fluids cannot have Schr\"odinger symmetry unless $z=2$. For generic values of $z$ there can be fluids with Lifshitz symmetry, and as a concrete example, we work out in detail the thermodynamics and fluid description of an ideal gas of Lifshitz particles and compute the speed of sound for the classical and quantum Lifshitz gasses.