The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid
Abstract
The considerations of the first paper of this series are modified so as to be consistent with the special theory of relativity. It is shown that the inertia of energy does not obviate the necessity for assuming the conservation of matter. Matter is to be interpreted as number of molecules, therefore, and not as inertia. Its velocity vector serves to define local proper-time axes, and the energy momentum tensor is resolved into proper-time and -space components. It is shown that the first law of thermodynamics is a scalar equation, and not the fourth component of the energy-momentum principle. Temperature and entropy also prove to be scalars. Simple relativistic generalizations of Fourier's law of heat conduction, and of the laws of viscosity are obtained from the requirements of the second law. The same considerations lead directly to the accepted relativistic form of Ohm's law.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The PPF can be seen as an anisotropic fluid with heat flux [33].
“As we shall see below, the PPF can actually be seen as an anisotropic fluid with heat flux [33].”
From Fluid dynamics in the warp drive spacetime geometry (2021) · cites this paper as [33]
The general stress-energy tensor of a relativistic fluid can be written as Tαβ = μ uα uβ + p hαβ + uα qβ + uβ qα + παβ, with hαβ = gαβ + ua ub.
“The general stress-energy tensor of a relativistic fluid can be written in the form [33,34]”
From Fluid dynamics in the warp drive spacetime geometry (2021) · cites this paper as [33]
Cited by
Sorted by citations
Gaussian reference fluid and interpretation of quantum geometrodynamics
Kucha, K. V., & Torre, C. G. (1991) · Physical Review D · doi:10.1103/physrevd.43.419 · Cited by 180 · see citing works
Fluid dynamics in the warp drive spacetime geometry
Santos-Pereira, O. L., Abreu, E. M. C., & Ribeiro, M. B. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-08921-3 · Cited by 29 · see citing works
- Authors
- Eckart, C.
- Affiliations
- University of Chicago (US)
- Corresponding author
- Eckart, Carl
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1940-11-15
- Volume
- 58
- Issue
- 10
- Pages
- 919-924
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2243423914
- Cited by
- 1,590
- References
- 0
- Citations by year
- 2026: 58 · 2025: 78 · 2024: 93 · 2023: 92 · 2022: 84 · 2021: 78 · 2020: 71 · 2019: 47 · 2018: 47 · 2017: 50 · 2016: 52 · 2015: 41 · 2014: 52 · 2013: 66 · 2012: 47
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Keywords
- non-equilibrium thermodynamics, relativistic thermodynamics, simple liquids, conservation of matter, proper time, energy-momentum tensor, first law of thermodynamics, Fourier's law of heat conduction, viscosity, second law of thermodynamics, special relativity
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
