Adiabatic hydrodynamics: the eightfold way to dissipation

By Felix M. Haehl, R. Loganayagam, M. Rangamani. 2015

145 citations recorded by the source corpus.

A bstractHydrodynamics is the low-energy effective field theory of any interacting quantum theory, capturing the long-wavelength fluctuations of an equilibrium Gibbs densitymatrix. 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a3ffa9ba95596a3121db8574ab3faaf2080d202a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Hong Liu
2. Xiao-Liang Qi
3. D. Stanford
4. R. Myers
5. P. Kovtun
6. Yingfei Gu
7. S. Hartnoll
8. S. Sachdev

In Nuclear and High Energy Physics

1. Xiao-Liang Qi
2. D. Stanford
3. Hong Liu
4. R. Myers
5. S. Sachdev
6. Yingfei Gu
7. S. Hartnoll
8. P. Kovtun

Citations in the corpus

• Effective field theory of dissipative fluids (2015, methodology): “Recent works [32, 33, 45, 46] also share some elements with our discussion here.”
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models (2016, background): “It would also be interesting to understand the relationship of this action to recent work on hydrodynamic actions [47, 48].”
• Relativistic magnetohydrodynamics (2017, background): “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”
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts (2016, background): “In relation to the above result, it has recently been pointed out that entropy conservation can be seen as the conservation of an effective Noether current associated to a certain symmetry emerging at late times [38, 39].”