Adiabatic hydrodynamics: the eightfold way to dissipation

Haehl, Felix M.; Loganayagam, Ramalingam; Rangamani, Mukund

Abstract

Hydrodynamics 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.

Citation

Haehl, F. M., Loganayagam, R., & Rangamani, M. (2015). Adiabatic hydrodynamics: the eightfold way to dissipation. Journal of High Energy Physics, 2015(5), Article 60. https://doi.org/10.1007/jhep05%282015%29060

• Journal Article Type: Article
• Acceptance Date: Apr 2, 2015
• Online Publication Date: May 12, 2015
• Publication Date: May 12, 2015
• Deposit Date: Apr 6, 2015
• Publicly Available Date: Apr 14, 2015
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 5
• Article Number: 60
• DOI: https://doi.org/10.1007/jhep05%282015%29060
• Keywords: Holography and quark-gluon plasmas, Effective field theories, Anomalies in Field and String Theories, Quantum Dissipative Systems.
• Public URL: https://durham-repository.worktribe.com/output/1410502
• Related Public URLs: http://arxiv.org/abs/1502.00636