Adiabatic hydrodynamics: the eightfold way to dissipation

Abstract

Hydrodynamics is the low-energy effective field theory of any interacting quantum theory, capturing the long-wavelength fluctuations of an equilibrium Gibbs density matrix. Conventionally, one views the effective dynamics in terms of the conserved currents, which should be expressed via the constitutive relations in terms of the fluid velocity and the intensive parameters such as the temperature, chemical potential, etc. . . However, not all constitutive relations are acceptable; one has to ensure that the second law of thermodynamics is satisfied on all physical configurations. In this paper, we provide a complete solution to hydrodynamic transport at all orders in the gradient expansion compatible with the second law constraint.The key new ingredient we introduce is the notion of adiabaticity, which allows us to take hydrodynamics off-shell. Adiabatic fluids are such that off-shell dynamics of the fluid compensates for entropy production. The space of adiabatic fluids is quite rich, and admits a decomposition into seven distinct classes. Together with the dissipative class this establishes the eightfold way of hydrodynamic transport. Furthermore, recent results guarantee that dissipative terms beyond leading order in the gradient expansion are agnostic of the second law. While this completes a transport taxonomy, we go on to argue for a new symmetry principle, an Abelian gauge invariance that guarantees adiabaticity in hydrodynamics. We suggest that this symmetry is the macroscopic manifestation of the microscopic KMS invariance. We demonstrate its utility by explicitly constructing effective actions for adiabatic transport. The theory of adiabatic fluids, we speculate, provides a useful starting point for a new framework to describe non-equilibrium dynamics, wherein dissipative effects arise by Higgsing the Abelian symmetry.

Relativistic magnetohydrodynamics

“…From a fundamental point of view, a number of recent developments in relativistic hydrodynamics have pushed the boundaries of the "traditional" theory, as described for example in the classic textbook [1]. These include: a systematic derivative expansion in hydrodynamics [2], an equivalence between hydrodynamics and black hole dynamics [3], the manifestation of chiral anomalies in hydrodynamic equations [4], the relevance of partition functions [5,6], elucidation of the role of the entropy current [7,8], new insights into relativistic hydrodynamic turbulence [9], convergence properties of the hydrodynamic expansion [10], and a classification of hydrodynamic transport coefficients [11]. It is reasonable to expect that the above insights will also lead to an improved understanding of the "traditional" MHD.…”

Emergent supersymmetry in local equilibrium systems

“…The effective action I EFT incorporates dissipations and retardation effects from the bath of short-lived degrees of freedom (which have been integrated out) in a medium. Its general structure has recently been used to derive from first principle the local second law of thermodynamics [9], and a new formulation of fluctuating hydrodynamics has been proposed in terms of such an EFT [10,11] (see also [12][13][14][15][16][17]). See also [18] for a review of applications to driven open systems.…”

“…To see this explicitly we must keep in mind that we should only select those terms in (B.27) which has the structure of (3.26). 15 There are three types of terms in (B.27):…”

Second-order hydrodynamics and universality in non-conformal holographic fluids

“…Fluids with simple gravity duals at strong coupling have been conjectured to obey a principle of minimal dissipation [43,92]. The observation that the lower bound on the shear viscosity over entropy density ratio is universally satisfied by a large class of holographic theories [22,[25][26][27]31] is a first hint in this direction since this ratio appears as coefficient of the leading contribution to the entropy production.…”

“…The relationsH = 0 and H = 0 found in this work are equivalent to H = 0 and 2λ 1 = κ − κ * . It was shown within an effective action approach to adiabatic hydrodynamics that these two relations must hold for perfect fluids that do not produce entropy [93]. Indeed, the Haack-Yarom identity, H = 0, seems to require either infinite coupling or adiabaticity.…”