Local thermodynamical equilibrium and relativistic dissipation

Salazar, José Félix; Zannias, T.

doi:10.1103/physrevd.106.103004

Cited by 5 publications

(3 citation statements)

References 67 publications

(378 reference statements)

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“…This equivalence is supported by the observation that, in both frames, the gradient expansion includes one set of scalars, one set of transverse vectors, and one set of TST tensors for each conserved charge [30]. Recent studies on relativistic local thermodynamic equilibrium (LTE) have established the equivalence between the "energy states" associated with the Landau frame and the "particle states" associated with the Eckart frame (see [31] and references therein).…”

Section: Hydrodynamic Frames and On-shell Equivalencesmentioning

confidence: 92%

Third-order relativistic fluid dynamics at finite density in a general hydrodynamic frame

Diles,

Miranda,

Mamani

et al. 2024

Eur. Phys. J. C

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The motion of water is governed by the Navier–Stokes equations, which are complemented by the continuity equation to ensure local mass conservation. In this work, we construct the relativistic generalization of these equations through a gradient expansion for a fluid with a conserved charge in a curved d-dimensional spacetime. We adopt a general hydrodynamic frame and introduce the irreducible-structure (IS) algorithm, which is based on derivatives of the expansion scalar and the shear and vorticity tensors. By this method, we systematically generate all permissible gradients up to a specified order and derive the most comprehensive constitutive relations for a charged fluid, accurate to third-order in the gradient expansion. These constitutive relations are formulated to apply to ordinary (nonconformal) and conformally invariant charged fluids. Furthermore, we examine the frame dependence of the transport coefficients for a nonconformal charged fluid up to the third order in the gradient expansion. The frame dependence of the scalar, vector, and tensor parts of the constitutive relations is obtained in terms of the (field redefinitions of the) fundamental hydrodynamic variables. Managing the frame dependencies of the constitutive relations is challenging due to their non-linear character. However, in the linear regime, the higher-order transformations become tractable, enabling the identification of a set of frame-invariant coefficients. Subsequently, the equations obtained in the linear regime are solved in momentum space, yielding dispersion relations for shear, sound, and diffusive modes for a non-conformal charged fluid, expressed in terms of a set of frame-invariant transport coefficients.

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Section: Hydrodynamic Frames and On-shell Equivalencesmentioning

confidence: 92%

Third-order relativistic fluid dynamics at finite density in a general hydrodynamic frame

Diles,

Miranda,

Mamani

et al. 2024

Eur. Phys. J. C

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“…7 For typographical convenience in (20) and in most of what follows, we suppress the dependance of the multipliers upon (J µ , T µν ). Moreover and without loss of generality we may set Λ 15 := 1 and this choice follows from the linear nature of equation ( 21) with respect to Λ.…”

Section: Divergence Fluids As Symmetric-hyperbolic Systemsmentioning

confidence: 99%

“…Once the above mentioned assumptions hold, then a clear thermodynamical interpretation of the multipliers (ζ, ζ µ ), follows naturally. (Subtleties associate with the thermodynamical concepts that we just defined are discussed in [20], where states satisfying the relativistic local thermodynamical equilibrium postulate are discussed in details).…”

Section: Examples Of Generating Functionsmentioning

confidence: 99%

Some remarks on relativistic fluids of divergence type

Zannias

Salazar

2023

Class. Quantum Grav.

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Relativistic fluids of divergence type constitute a special class of fluids whose states are determined from the knowledge of a scalar generating function $\chi $ and the dissipation tensor $I^{\mu\nu}$ i.e. a second rank, symmetric and traceless tensor. Both $(\chi, I^{\mu\nu})$ depend upon fourteen variables, known in the literature as Lagrange multipliers, and these multipliers satisfy a symmetric, quasilinear, first order system determined by $(\chi, I^{\mu\nu})$. For particular choices of the generating function $\chi$, this system can be symmetric-hyperbolic and causal. We show in this work that this characteristic property of fluids of divergence type originates in the overdetermined nature of their dynamical equations. Combining their overdetermined nature with the work of K.O. Friedrichs on overdetermined system of conservation laws with more recent work by Boillat, Ruggeri and coworkers, we prove that fluids of divergence type are locally determined by a vector potential depending upon the Lagrange multipliers. For the case where the dynamical variables describing fluid states contain a symmetric energy momentum tensor, this vector potential is the gradient of a scalar field and this field is precisely the generating function $\chi $ introduced by Pennisi and independently by Geroch and Lindblom. Examples of scalar generating function $\chi$ are discussed where this system is a symmetric hyperbolic and causal system in an open vicinity of equilibrium states.

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Recent developments in mathematical aspects of relativistic fluids

Disconzi

2024

Living Rev Relativ

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We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.

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Local thermodynamical equilibrium and relativistic dissipation

Cited by 5 publications

References 67 publications

Third-order relativistic fluid dynamics at finite density in a general hydrodynamic frame

Third-order relativistic fluid dynamics at finite density in a general hydrodynamic frame

Some remarks on relativistic fluids of divergence type

Recent developments in mathematical aspects of relativistic fluids

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