Thermodynamics Since Einstein

Chih-Yueh WANG


Relativistic thermodynamics is a relatively unknown theory. Thermodynamic laws apply only to quasi-static processes that quickly change between states that are in a long-term equilibrium. However, special relativity postulates that the propagation speed of physical signals is constrained, thus limiting the speed of change in thermal states. Einstein was especially interested in the concept of temperature and the transformation formula of thermodynamic quantities in a moving frame of reference, having inspired numerous investigations for two centuries. This article reviews the historical development of relativistic thermodynamics since Einstein, beginning from the initial idea of Planck-Einstein in which a moving body warms up, to the notion of Blanusa-Ott in which a moving body cools down, and to that of Landsberg in which the temperature remains unchanged—depending on how the observer’s thermometer is defined. Current research focuses on identifying the correct form of relativistic Maxwell distribution to validate the related theory. Recent computational results using molecular dynamic simulations and their relevance to astrophysics are outlined as well.


Relativistic thermodynamics; Special relativity; Molecular dynamics

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Anderson, J. L. (1964). Relativity principles and the role of coordinates in Physics. In H. Y. Chiu & W. F. Hoffmann (Eds.), Gravitation and relativity (pp.175-194). N.Y.: W. A. Benjamin.

Balescu, R. (1968). Relativistic statistical thermodynamics. Physica, 40, 309-338.

Biro, T. S. (2011). Is there a temperature? New York, Dordrecht, Heidelberg, London: Springer.

Blanusa, D. (1947). Sur les paradoxes de la notion d éEnergie. Glasnik mat.-fiz i astr., 2, 249-250.

Cubero, D., Casado-Pascual, J., Dunkel, P., Talkner, P., & Hänggi, P. (2007). Thermal equilibrium and statistical thermometers in special relativity. Physical Review Letter, 99, 170601.

Dunkel, J., Talkner, P., & Hänggi, P. (2007). Relative entropy, haar measures and relativistic canonical velocity distributions. New Journal of Physics, 9, 144.

Einstein, A. (1905). Zur Elektrodynamik bewegter Körper.Annalen der Physik, 322(10), 891-921.

Einstein, A. (1907). Über das Relativitätsprinzip und die aus Demselben Gezogenen Folgerungen. Jahrbuch der Radioaktivität und Elektronik, 4, 411-462.

Ghodrat, M., & Montakhab, A. (2010). Time parameterization and stationary distributions in a relativistic gas. Physical Review E, 82, 011110.

Ghodrat, M., & Montakhab, A. (2011). Molecular dynamics simulation of a relativistic gas: Thermostatistical properties. Computer Physics Communications, 182, 1909-1913.

Horwitz, L. P., Schieve, W. C., & Piron, C. (1981). Gibbs ensembles in relativistic classical and quantum mechanics. Annals of Physics, 137(2), 306-340.

Horwitz, L. P., Shashoua, S., & Schieve, W. C. (1989). A manifestly covariant relativistic boltzmann equation for the evolution of a system of events. Physica A: Statistical Mechanics and its Applications, 16(2), 300-338.

Itoh, N., Kohyama, Y., & Nozawa, S. (1998). Relativistic eorrections to the sunyaev-zeldovich effect for clusters of galaxies. Astrophysical Journal, 502, 7-15.

Jüttner, F. (1911). Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie. Annalen der Physik, 339(5), 856-882.

Landsberg, P. T. (1966). Does a moving body appear cool? Nature, 212, 571-572.

Landsberg, P. T. (1967). Does a moving body appear cool? Nature, 214, 903-904.

Landsberg, P. T. (1968). Special relativity. Nature, 217, 883-883.

Landsberg, P. T. (1981). Einstein and statistical thermodynamics I. Relativistic thermodynamics. European Journal of Physics, 2(4), 203-207.

Landsberg, P. T. (1981). Einstein and statistical thermodynamics, III. The diffusion-mobility relation in semiconductors. European Journal of Physics, 2(4), 213-219.

Landsberg, P. T. (1981). Einstein and statistical thermodynamics. II. Oscillator quantization. European Journal of Physics, 2(4), 208-212.

Liu, C. (1992). Einstein and relativistic thermodynamics in 1952: A historical and critical study of a strange episode in the history of modern physics. British Journal for the History of Science, 25, 185-206.

Ott, H. (1963). Lorentz transformation der warme und der temperatur. Zeitschrift für Physik, 175, 70-104.

Planck, M. (1907). Zur dynamik bewegter systeme.Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften, (29), 542-570.

Planck, M. (1908). Zur dynamik bewegter systeme. Annalen der Physik, 331(6), 1-34.

Planck, M. (1910). Acht vorlesungen über theoretische physik: Gehalten an der Columbia university in the city of New York im frühjahr 1909. Leipzig: S. Hirzel.

Prokhorov, D., Colafrancesco, S., Akahori, T., Yoshikawa, K., Nagataki, S., & Seon, K.-I. (2011). Can electron distribution functions be derived through the Sunyaev-Zel’dovich effect? Astronomy and Astrophysics, 529, A39 .

Treder, H.-J. (1977). Die Strahlungstemperatur bewegter Koerper. Annalen der Physik, 489(1), 23-29.

Van Kampen, N. G. (1992). Stochastic processes in physics and chemistry (2nd ed.). Amsterdam: Elsevier.

Von Mosengeil, K. (1907). Theorie der stationaeren Strahlung in einem gleichfoermig bewegten Hohlraum. Annalen der Physik, 327(5), 867-904.



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