Built on

L. Onsager, “Reciprocal Relations in Irreversible Processes. I,” Phys. Rev. 37
1931
Earlier work this paper cites.
L. Onsager, “Reciprocal Relations in Irreversible Processes. II,” Phys. Rev. 38
1931
Earlier work this paper cites.
H. B. G. Casimir, “On Onsager’s Principle of Microscopic Reversibility,” Rev. Mod. Phys. 17
1945
Earlier work this paper cites.
C. Eckart, “The Thermodynamics of Irreversible Processes. IV. The Theory of Elasticity and Anelasticity,” Phys. Rev. 73
1948
Earlier work this paper cites.
I. Müller, “Zum Paradoxon der Wärmeleitungstheorie,” Z. Phys. 198
1967
Earlier work this paper cites.
W. Israel, “Nonstationary irreversible thermodynamics: A Causal relativistic theory,” Annals Phys. 100
1976
Earlier work this paper cites.
B. Carter and H. Quintana, “Gravitational And Acoustic Waves In An Elastic Medium,” Phys. Rev. D 16
1977
Earlier work this paper cites.

Similar

M. Kranys, “Relativistic elasticity of dissipative media and its wave propagation modes” J. Phys. A. Math. Gen. 10
Original
1977
Cited alongside, same era.
W. Israel and J. M. Stewart, “Transient relativistic thermodynamics and kinetic theory,” Annals Phys. 118
1979
Cited alongside, same era.
L. D. Landau and E. M. Lifshitz, “Statistical Physics, Part 1,” Butterworth-Heinemann (1980)
1980
Cited alongside, same era.
S. R. de Groot and P. Mazur, “Non-Equilibrium Thermodynamics,” Dover (1984)
1984
Cited alongside, same era.
L. D. Landau and E. M. Lifshitz, “Theory of Elasticity,” Butterworth-Heinemann (1986)
1986
Cited alongside, same era.
L. D. Landau and E. M. Lifshitz, “Fluid Mechanics,” Butterworth-Heinemann (1987)

Then

P. K. Kovtun and A. O. Starinets, “Quasinormal modes and holography,” Phys. Rev. D 72
2005
Later among the works it cites.
G. S. Denicol, T. Kodama, T. Koide and Ph. Mota, “Non-Linearity Induced by Finite Size of Fluid Cell in Causal Dissipative Hydrodynamics,” J. Phys. G 35
Original
2008
Later among the works it cites.
R. Baier, P. Romatschke, D. T. Son, A. O. Starinets and M. A. Stephanov, “Relativistic viscous hydrodynamics, conformal invariance, and holography,” JHEP 0804
Original
2008
Later among the works it cites.
T. Azeyanagi, M. Fukuma, H. Kawai and K. Yoshida, “Universal description of viscoelasticity with foliation preserving diffeomorphisms,” Phys. Lett. B 681
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2009
Later among the works it cites.
P. Romatschke, “New Developments in Relativistic Viscous Hydrodynamics,” Int. J. Mod. Phys. E 19

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2011

Relativistic viscoelastic fluid mechanics

Fukuma, Masafumi, Sakatani, Yuho

Understand

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics.

After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit.
Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied.
We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski spacetime become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems.

Built on

L. Onsager, “Reciprocal Relations in Irreversible Processes. I,” Phys. Rev. 37
1931
Earlier work this paper cites.
L. Onsager, “Reciprocal Relations in Irreversible Processes. II,” Phys. Rev. 38
1931
Earlier work this paper cites.
H. B. G. Casimir, “On Onsager’s Principle of Microscopic Reversibility,” Rev. Mod. Phys. 17
1945
Earlier work this paper cites.
C. Eckart, “The Thermodynamics of Irreversible Processes. IV. The Theory of Elasticity and Anelasticity,” Phys. Rev. 73
1948
Earlier work this paper cites.
I. Müller, “Zum Paradoxon der Wärmeleitungstheorie,” Z. Phys. 198
1967
Earlier work this paper cites.
W. Israel, “Nonstationary irreversible thermodynamics: A Causal relativistic theory,” Annals Phys. 100
1976
Earlier work this paper cites.
B. Carter and H. Quintana, “Gravitational And Acoustic Waves In An Elastic Medium,” Phys. Rev. D 16
1977
Earlier work this paper cites.

Similar

M. Kranys, “Relativistic elasticity of dissipative media and its wave propagation modes” J. Phys. A. Math. Gen. 10
Original
1977
Cited alongside, same era.
W. Israel and J. M. Stewart, “Transient relativistic thermodynamics and kinetic theory,” Annals Phys. 118
1979
Cited alongside, same era.
L. D. Landau and E. M. Lifshitz, “Statistical Physics, Part 1,” Butterworth-Heinemann (1980)
1980
Cited alongside, same era.
S. R. de Groot and P. Mazur, “Non-Equilibrium Thermodynamics,” Dover (1984)
1984
Cited alongside, same era.
L. D. Landau and E. M. Lifshitz, “Theory of Elasticity,” Butterworth-Heinemann (1986)
1986
Cited alongside, same era.
L. D. Landau and E. M. Lifshitz, “Fluid Mechanics,” Butterworth-Heinemann (1987)