Abstract
Does heat have inertia? This question is at the core of a long-standing controversy on Eckart's dissipative relativistic hydrodynamics. Here I show that the troublesome inertial term in Eckart’s heat flux arises only if one insists on defining thermal diffusivity as a spacetime constant. I argue that this is not the most natural definition, and that all confusion disappears if one considers, instead, the space-dependent comoving diffusivity, in line with the fact that, in the presence of gravity, space is an inhomogeneous medium.
Similar content being viewed by others
References
C. Eckart, Phys. Rev. 58, 919 (1940).
Pham Mau Quan, Ann. Mat. Pura Appl. 38, 121 (1955).
J.-F. Bennoun, Ann. Inst. H. Poincaré 3, 41 (1965).
L.D. Landau, E. Lifshitz, Fluid Mechanics (Butterworth-Heinemann, 1987).
J. Ehlers, Kinetic theory of gases in general relativity theory, in Lectures in Statistical Physics (Springer Berlin/Heidelberg, 1974) pp. 78--105.
W. Israel, Ann. Phys. 100, 310 (1976).
W. Israel, J.M. Stewart, Ann. Phys. 118, 341 (1979).
W.A. Hiscock, L. Lindblom, Phys. Rev. D 31, 725 (1985).
N.G. Van Kampen, J. Stat. Phys. 46, 709 (1987).
A. Sandoval-Villalbazo, A. Garcia-Perciante, L. Garcia-Colin, Physica A 388, 3765 (2009).
L. García-Colín, A. Sandoval-Villalbazo, J. Non - Equilib. Thermodyn. 31, 11 (2006).
L. García-Colín, A. Sandoval-Villalbazo, J. Non - Equilib. Thermodyn. 32, 187 (2007).
W. Muschik, H.-H. von Borzeszkowski, J. Non - Equilib. Thermodyn. 32, 181 (2007).
A.L. Garcia-Perciante, L. Garcia-Colin, A. Sandoval-Villalbaz, Gen. Relativ. Gravit. 41, 1645 (2009).
N. Andersson, G. Comer, Proc. R. Soc. London A 466, 1373 (2010).
M. Smerlak, A. Youssef, The overdamped limit of the relativistic Kramers equation, in preparation.
H.D. Weymann, Am. J. Phys. 35, 488 (1967).
R. Geroch, J. Math. Phys. 36, 4226 (1995).
R. Tolman, P. Ehrenfest, Phys. Rev. 36, 1791 (1930).
N. Van Kampen, J. Phys. Chem. Solids 49, 673 (1988).
E. Bringuier, Eur. J. Phys. 32, 975 (2011).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Smerlak, M. On the inertia of heat. Eur. Phys. J. Plus 127, 72 (2012). https://doi.org/10.1140/epjp/i2012-12072-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2012-12072-4