Relativistic hydrodynamic fluctuations from an effective action: Causality, stability, and the information current
Abstract
Causality is necessary for retarded Green’s functions to remain retarded in all inertial frames in relativity, which ensures that dissipation of fluctuations is a Lorentz invariant concept. For first-order Bemfica, Disconzi, Noronha, and Kovtun theories with stochastic fluctuations, introduced via the Schwinger-Keldysh formalism, we show that imposing causality and stability leads to correlation functions of hydrodynamic fluctuations that only display the expected physical properties at small frequencies and wave number, i.e., within the expected regime of validity of the first-order approach. For second-order theories of the Israel and Stewart type, constructed using the information current such that entropy production is always non-negative, a stochastic formulation is presented using the Martin-Siggia-Rose approach where imposing causality and stability leads to correlators with the desired properties. We also show how Green’s functions can be determined from such an action. We identify a Z2 symmetry, analogous to the Kubo-Martin-Schwinger symmetry, under which this Martin-Siggia-Rose action is invariant. This modified Kubo-Martin-Schwinger symmetry provides a new guide for the effective action formulation of hydrodynamic systems with dynamics not solely governed by conservation laws. Furthermore, this symmetry ensures that the principle of detailed balance is valid in a covariant manner. We employ the new symmetry to furthermore »
- Publication Date:
- Research Org.:
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); MUSES Collaboration; National Science Foundation (NSF)
- OSTI Identifier:
- 2251536
- Alternate Identifier(s):
- OSTI ID: 2283628
- Grant/Contract Number:
- SC0021301; SC0023861; OAC-2103680; NSF PHY-1748958
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. D.
- Additional Journal Information:
- Journal Name: Physical Review. D. Journal Volume: 108 Journal Issue: 11; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Relativistic heavy-ion collisions; Relativistic hydrodynamics; Stochastic differential equations
Citation Formats
Mullins, Nicki, Hippert, Mauricio, Gavassino, Lorenzo, and Noronha, Jorge. Relativistic hydrodynamic fluctuations from an effective action: Causality, stability, and the information current. United States: N. p., 2023.
Web. doi:10.1103/PhysRevD.108.116019.
Mullins, Nicki, Hippert, Mauricio, Gavassino, Lorenzo, & Noronha, Jorge. Relativistic hydrodynamic fluctuations from an effective action: Causality, stability, and the information current. United States. https://doi.org/10.1103/PhysRevD.108.116019
Mullins, Nicki, Hippert, Mauricio, Gavassino, Lorenzo, and Noronha, Jorge. Fri .
"Relativistic hydrodynamic fluctuations from an effective action: Causality, stability, and the information current". United States. https://doi.org/10.1103/PhysRevD.108.116019.
@article{osti_2251536,
title = {Relativistic hydrodynamic fluctuations from an effective action: Causality, stability, and the information current},
author = {Mullins, Nicki and Hippert, Mauricio and Gavassino, Lorenzo and Noronha, Jorge},
abstractNote = {Causality is necessary for retarded Green’s functions to remain retarded in all inertial frames in relativity, which ensures that dissipation of fluctuations is a Lorentz invariant concept. For first-order Bemfica, Disconzi, Noronha, and Kovtun theories with stochastic fluctuations, introduced via the Schwinger-Keldysh formalism, we show that imposing causality and stability leads to correlation functions of hydrodynamic fluctuations that only display the expected physical properties at small frequencies and wave number, i.e., within the expected regime of validity of the first-order approach. For second-order theories of the Israel and Stewart type, constructed using the information current such that entropy production is always non-negative, a stochastic formulation is presented using the Martin-Siggia-Rose approach where imposing causality and stability leads to correlators with the desired properties. We also show how Green’s functions can be determined from such an action. We identify a Z2 symmetry, analogous to the Kubo-Martin-Schwinger symmetry, under which this Martin-Siggia-Rose action is invariant. This modified Kubo-Martin-Schwinger symmetry provides a new guide for the effective action formulation of hydrodynamic systems with dynamics not solely governed by conservation laws. Furthermore, this symmetry ensures that the principle of detailed balance is valid in a covariant manner. We employ the new symmetry to further clarify the connection between the Schwinger-Keldysh and Martin-Siggia-Rose approaches, establishing a precise link between these descriptions in second-order theories of relativistic hydrodynamics. Finally, the modified Kubo-Martin-Schwinger symmetry is used to determine the corresponding action describing diffusion in Israel-Stewart theories in a general hydrodynamic frame.},
doi = {10.1103/PhysRevD.108.116019},
journal = {Physical Review. D.},
number = 11,
volume = 108,
place = {United States},
year = {Fri Dec 22 00:00:00 EST 2023},
month = {Fri Dec 22 00:00:00 EST 2023}
}
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