Ultrarelativistic Gas with Zero Chemical Potential

In this work, we propose a set of conditions such that an ultrarelativistic classical gas can present a photon-like behavior. This is achieved by assigning a zero chemical potential to the ultrarelativistic ideal gas. The resulting behavior is similar to that of a Wien photon gas. It is found to be possible only for gases made of very lightweight particles such as neutrinos, as long as we treat them as classical particles, and it depends on the spin degeneracy factor. This procedure allows establishing an analogy between an evaporating gas and the cavity radiation.

[1]  U. Klein,et al.  What is the limit ℏ → 0 of quantum theory? , 2011, 1201.0150.

[2]  M. Planck.  Ueber das Gesetz der Energieverteilung im Normalspectrum , 1901 .

[3]  L. Horwitz,et al.  Gibbs ensembles in relativistic classical and quantum mechanics , 1981 .

[4]  A. Einstein.  Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)] , 2005, Annalen der Physik.

[5]  S. Rice,et al.  Heat, Thermodynamics, and Statistical Physics , 1963 .

[6]  F. Debbasch.  Equilibrium distribution function of a relativistic dilute perfect gas , 2008 .

[7]  Minimum Entropy Production of Neutrino Radiation in the Steady State , 1999 .

[8]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[9]  Gonzalo Ares de Parga,et al.  Relativistic Statistical Mechanics vs. Relativistic Thermodynamics , 2011, Entropy.

[10]  Horst Stöcker,et al.  Thermodynamics and Statistical Mechanics , 2002 .

[11]  A. Balantekin,et al.  On the Properties of Neutrinos , 2018, Annual Review of Nuclear and Particle Science.

[12]  F. Jüttner.  Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie , 1911 .

[13]  O. Passon,et al.  Planck’s radiation law, the light quantum, and the prehistory of indistinguishability in the teaching of quantum mechanics , 2017, 1703.05635.

[14]  R. Hagedorn,et al.  Statistical thermodynamics of strong interactions at high-energies. 2. Momentum spectra of particles produced in pp-collisions , 1965 .

[15]  P. Landsberg,et al.  IDEAL RELATIVISTIC BOSE CONDENSATION , 1965 .

[16]  F. Mandl,et al.  Statistical Physics, 2nd Edition , 1988 .