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Title: Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow

Abstract

We present a detailed and self-contained analysis of the universal SchwingerKeldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction. We write an effective action for appropriate hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries to be imposed. The constraints imposed by fluctuation-dissipation theorem are manifest in our formalism. Consequently, the action reproduces hydrodynamic constitutive relations consistent with the local second law at all orders in the derivative expansion, and captures the essential elements of the eightfold classification of hydrodynamic transport of. We demonstrate how to recover the hydrodynamic entropy and give predictions for the non-Gaussian hydrodynamic fluctuations. The basic ingredients of our construction involve (i) doubling of degrees of freedom a la Schwinger-Keldysh, (ii) an emergent gauge U(1)T symmetry associated with entropy which is encapsulated in a Noether current a la Wald, and (iii) a BRST/topological supersymmetry imposing the fluctuation-dissipation theorem a la Parisi-Sourlas. The overarching mathematical framework for our construction is provided by the balanced equivariant cohomology of thermal translations, which captures the basic constraints arising from the Schwinger-Keldysh doubling, and the thermal Kubo-Martin-Schwinger relations. All these features are conveniently implemented in a covariant superspace formalism. Anmore » added benefit is that the second law can be understood as being due to entropy inflow from the Grassmann-odd directions of superspace.« less

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
  2. International Centre for Theoretical Sciences (ICTS-TIFR) (India)
  3. Univ. of California, Davis, CA (United States). Dept. of Physics
Publication Date:
Research Org.:
Univ. of California, Davis, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1611306
Grant/Contract Number:  
SC0009999
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 10; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Effective Field Theories; Topological Field Theories; Quantum Dissipative Systems; AdS-CFT Correspondence

Citation Formats

Haehl, Felix M., Loganayagam, R., and Rangamani, Mukund. Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow. United States: N. p., 2018. Web. doi:10.1007/jhep10(2018)194.
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Haehl, Felix M., Loganayagam, R., & Rangamani, Mukund. Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow. United States. https://doi.org/10.1007/jhep10(2018)194
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Haehl, Felix M., Loganayagam, R., and Rangamani, Mukund. Tue . "Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow". United States. https://doi.org/10.1007/jhep10(2018)194. https://www.osti.gov/servlets/purl/1611306.
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@article{osti_1611306,
title = {Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow},
author = {Haehl, Felix M. and Loganayagam, R. and Rangamani, Mukund},
abstractNote = {We present a detailed and self-contained analysis of the universal SchwingerKeldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction. We write an effective action for appropriate hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries to be imposed. The constraints imposed by fluctuation-dissipation theorem are manifest in our formalism. Consequently, the action reproduces hydrodynamic constitutive relations consistent with the local second law at all orders in the derivative expansion, and captures the essential elements of the eightfold classification of hydrodynamic transport of. We demonstrate how to recover the hydrodynamic entropy and give predictions for the non-Gaussian hydrodynamic fluctuations. The basic ingredients of our construction involve (i) doubling of degrees of freedom a la Schwinger-Keldysh, (ii) an emergent gauge U(1)T symmetry associated with entropy which is encapsulated in a Noether current a la Wald, and (iii) a BRST/topological supersymmetry imposing the fluctuation-dissipation theorem a la Parisi-Sourlas. The overarching mathematical framework for our construction is provided by the balanced equivariant cohomology of thermal translations, which captures the basic constraints arising from the Schwinger-Keldysh doubling, and the thermal Kubo-Martin-Schwinger relations. All these features are conveniently implemented in a covariant superspace formalism. An added benefit is that the second law can be understood as being due to entropy inflow from the Grassmann-odd directions of superspace.},
doi = {10.1007/jhep10(2018)194},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2018,
place = {United States},
year = {Tue Oct 30 00:00:00 EDT 2018},
month = {Tue Oct 30 00:00:00 EDT 2018}
}
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https://doi.org/10.1007/jhep10(2018)194
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    Elasticity bounds from effective field theory
    journal, September 2019

    Relativistic Hydrodynamic Fluctuations
    text, January 2019

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