Out-of-equilibrium hydrodynamics with and without boost symmetry

Abstract

In this thesis, we explore the role of symmetries in hydrodynamics by studying certain properties of relativistic and non-relativistic fluids. In the first part of the thesis, we examine the theory of relativistic magnetohydrodynamics (Maxwell electromagnetism coupled to hydrodynamics) and its low temperature incarnation, force-free electrodynamics, reformulated in the language of higher-form symmetries and discuss the advantages of such a scheme. Using this framework, we analyse the regime of validity of force-free electrodynamics by evaluating the lifetime of the non-conserved electric field operator via a holographic model sharing the same global symmetries as that of a plasma. We are able to explicitly calculate the lifetime of the electric field, both parallel and perpendicular to the magnetic field, and find that there are indeed no long-lived modes that interfere with a hydrodynamic description of force-free electrodynamics. In the second part of the thesis, we study the thermodynamic properties of non-relativistic Lifshitz fluids with an arbitrary dynamic exponent z (encoding the anisotropy in the scaling of time and space coordinates). We study energy transport in such fluids far from equilibrium after performing a local quench between two semi-infinite fluid reservoirs. We find that the late time energy flow is universal and accommodated via a steady state occupying an expanding central region between outgoing shock and rarefaction waves (a non-equilibrium steady state), as seen previously for relativistic scale invariant fluids. Armed with an equation of state for a perfect Lifshitz fluid with an arbitrary z and moving with a velocity v, we proceed to study its holographic dual using the well established Einstein-Maxwell-Dilaton model. We find that the fluid velocity appears as the chemical potential, conjugate to the dual momentum density and the solutions represent a physically distinct class of black branes possessing a linear momentum, different from boosting a static brane.