Towards Hydrodynamics without an Entropy Current

Abstract

We present a generating functional which describes the equilibrium thermodynamic response of a relativistic system to external sources. A variational principle gives rise to constraints on the response parameters of relativistic hydrodynamics without making use of an entropy current. Our method reproduces and extends results available in the literature. It also provides a technique for efficiently computing n-point zero-frequency correlation functions within the hydrodynamic derivative expansion without the need to explicitly solve the equations of hydrodynamics.

Emergent supersymmetry in local equilibrium systems

“…While this paper is in preparation we learned that overlapping results have been obtained by Kristan Jensen, Natalia Pinzani-Fokeeva, and Amos Yarom [35].…”

Effective actions for anomalous hydrodynamics

“…23 Our discussion so far has been sufficiently general and has made no reference to the specific form of S eff ; the next task is to specify this discussion to the non-dissipative effective action derived in the previous sections.…”

“…In [22,23] it has been shown how the hydrodynamic constitutive relations are constrained by the requirement of the existence of a stationary flow on arbitrary spatially (slowly) varying backgrounds. Furthermore, the physics of such time-independent flows can be encapsulated in an equilibrium partition function of the sources.…”

“…The logic exploited in [22,23] is that equilibrium configurations of a fluid in the presence of arbitrary time-independent spatially varying sources (which thereby allow non-trivial stationary fluid flows) can be equivalently described by a partition function of the sources. By writing down the most general partition function compatible with the symmetries in a systematic low energy gradient expansion, together with introduction of parity-odd terms to account for anomalies, it was shown in [22] that all known effects of global anomalies in hydrodynamics could be captured explicitly.…”

“…There is no low energy Lagrangian, and the stress-energy tensor and conserved currents are not constructed from more fundamental degrees of freedom of a true effective field theory (the equilibrium partition functions of [22,23] are functionals of JHEP03 (2014)034 background sources). It is therefore interesting to examine the extent to which an effective field theory of hydrodynamics can be formulated in terms of appropriate degrees of freedom.…”