Erratum to: “Derivation of covariant dissipative fluid dynamics in the renormalization-group method” [Phys. Lett. B 646 (2007) 134]

Tsumura, Kyosuke; Kunihiro, Teiji; Ohnishi, Kazuaki

doi:10.1016/j.physletb.2007.10.003

Cited by 29 publications

(74 citation statements)

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“…Another form of global equilibrium, which is a special case of eq. (2.6) is the pure rotation, with b = (1/T 0 , 0) and ̟ ∝ ω 0 /T 0 such that: 8) which has recently raised much attention for fermions [43,44]. In order to represent a physical fluid at equilibrium, β must be a timelike vector.…”

Section: Jhep10(2017)091mentioning

confidence: 99%

General equilibrium second-order hydrodynamic coefficients for free quantum fields

Buzzegoli

Grossi

Becattini

2017

J. High Energ. Phys.

135

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We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called "Kubo formulae". We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term.

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Section: Jhep10(2017)091mentioning

confidence: 99%

General equilibrium second-order hydrodynamic coefficients for free quantum fields

Buzzegoli

Grossi

Becattini

2017

J. High Energ. Phys.

135

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“…This also means that the EOS is given by, p 0 = p 0 (e 0 , n 0 ), and the temperature and chemical potential are fixed by the equilibrium state. Alternatively one could use different matching conditions [13] or even different thermodynamical theories, see for example Refs. [14,15,16].…”

Section: The Methods Of Momentsmentioning

confidence: 99%

Second order dissipative fluid dynamics from kinetic theory

Betz

Denicol

Koide

et al. 2011

EPJ Web of Conferences

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Abstract.We derive the equations of second order dissipative fluid dynamics from the relativistic Boltzmann equation following the method of W. Israel and J. M. Stewart [1]. We present a frame independent calculation of all first-and second-order terms and their coefficients using a linearised collision integral. Therefore, we restore all terms that were previously neglected in the original papers of W. Israel and J. M. Stewart.

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“…We give a general proof without recourse to numerical calculations that the hydrodynamic equations obtained in our formalism certainly ensure the stability of steady states including the thermal equilibrium state, on the basis of the positive definiteness of the inner product. * ) In a previous short communication, 36) we discussed the equation obtained with an erroneous setting θ = −π/4. We note that this choice is not appropriate and the resulting equation should be abandoned since −π/4 is out of the range of θ (4 .…”

Section: Discussionmentioning

confidence: 99%

First-Principles Derivation of Stable First-Order Generic-Frame Relativistic Dissipative Hydrodynamic Equations from Kinetic Theory by Renormalization-Group Method

Tsumura¹,

Kunihiro²

2011

Progress of Theoretical Physics

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We derive first-order relativistic dissipative hydrodynamic equations from the relativistic Boltzmann equation by the renormalization-group (RG) method. We introduce a macroscopic-frame vector, which does not necessarily coincide with the flow velocity, to specify the local rest frame on which the macroscopic dynamics is described. The five hydrodynamic modes are naturally identified with the same number of zero modes of the linearized collision operator, i.e., the collision invariants. After defining the inner product in the function space spanned by the distribution function, the higher-order terms, which give rise to the dissipative effects, are constructed so that they are precisely orthogonal to the zero modes in terms of the inner product: Here, no ansatzs, such as the so-called conditions of fit used in the standard methods in an ad hoc way, are necessary. We elucidate that the Burnett term does not affect the hydrodynamic equations owing to the very nature of the hydrodynamic modes as the zero modes. Then, applying the RG equation, we obtain the hydrodynamic equation in a generic frame specified by the macroscopic-frame vector, as the coarse-grained and covariant equation. Our generic hydrodynamic equation reduces to hydrodynamic equations in various local rest frames, including the energy and particle frames with a choice of the macroscopic-frame vector. We find that our equation in the energy frame coincides with that of Landau and Lifshitz, while the derived equation in the particle frame is slightly different from that of Eckart, owing to the presence of the dissipative internal energy. We prove that the Eckart equation is not compatible with the underlying relativistic Boltzmann equation. The proof is made on the basis of the observation that the orthogonality condition to the zero modes coincides with the ansatzs posed on the dissipative parts of the energy-momentum tensor and the particle current in the phenomenological equations. We also present an analytic proof that all our equations ensure the stability of steady states including the thermal equilibrium state owing to the positive definiteness of the inner product.

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Erratum to: “Derivation of covariant dissipative fluid dynamics in the renormalization-group method” [Phys. Lett. B 646 (2007) 134]

Cited by 29 publications

References 0 publications

General equilibrium second-order hydrodynamic coefficients for free quantum fields

General equilibrium second-order hydrodynamic coefficients for free quantum fields

Second order dissipative fluid dynamics from kinetic theory

First-Principles Derivation of Stable First-Order Generic-Frame Relativistic Dissipative Hydrodynamic Equations from Kinetic Theory by Renormalization-Group Method

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