Bulk viscosity in relativistic fluids: from thermodynamics to hydrodynamics. (arXiv:2003.04609v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Gavassino_L/0/1/0/all/0/1">Lorenzo Gavassino</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Antonelli_M/0/1/0/all/0/1">Marco Antonelli</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Haskell_B/0/1/0/all/0/1">Brynmor Haskell</a>
The approach of extended irreversible thermodynamics consists of promoting
the dissipative fluxes to non-equilibrium thermodynamic variables. In a
relativistic context, this naturally leads to the formulation of the theory of
Israel and Stewart (1979), which is, to date, one of the most successful
theories for relativistic dissipation. Although the generality of the principle
makes it applicable to any dissipative fluid, a connection of the
Israel-Stewart theory with microphysics has been established, through kinetic
theory, only for the case of ideal quantum gases. By performing a convenient
change of variables, we provide, for the case of bulk viscosity, an equivalent
reformulation of the equations at the basis of extended irreversible
thermodynamics. This approach maps any thermodynamic process which contributes
to the bulk viscosity into a set of chemical reactions, whose reaction
coordinates are abstract parameters describing the displacement from local
thermodynamic equilibrium of the fluid element. We apply our new formalism to
the case of the relativistic fluids, showing that the Israel-Stewart model for
bulk viscosity is just the second-order expansion of a minimal model belonging
to a larger class of non-perturbative theories for bulk viscosity which include
the nuclear-reaction-mediated bulk viscosity of neutron star matter as a
particular case. Furthermore, we show with concrete examples that our formalism
provides new ways of computing the bulk viscosity directly and defines a simple
prescription for constructing the Israel-Stewart model for a generic
bulk-viscous fluid.
The approach of extended irreversible thermodynamics consists of promoting
the dissipative fluxes to non-equilibrium thermodynamic variables. In a
relativistic context, this naturally leads to the formulation of the theory of
Israel and Stewart (1979), which is, to date, one of the most successful
theories for relativistic dissipation. Although the generality of the principle
makes it applicable to any dissipative fluid, a connection of the
Israel-Stewart theory with microphysics has been established, through kinetic
theory, only for the case of ideal quantum gases. By performing a convenient
change of variables, we provide, for the case of bulk viscosity, an equivalent
reformulation of the equations at the basis of extended irreversible
thermodynamics. This approach maps any thermodynamic process which contributes
to the bulk viscosity into a set of chemical reactions, whose reaction
coordinates are abstract parameters describing the displacement from local
thermodynamic equilibrium of the fluid element. We apply our new formalism to
the case of the relativistic fluids, showing that the Israel-Stewart model for
bulk viscosity is just the second-order expansion of a minimal model belonging
to a larger class of non-perturbative theories for bulk viscosity which include
the nuclear-reaction-mediated bulk viscosity of neutron star matter as a
particular case. Furthermore, we show with concrete examples that our formalism
provides new ways of computing the bulk viscosity directly and defines a simple
prescription for constructing the Israel-Stewart model for a generic
bulk-viscous fluid.
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