Abstract: A scale invariant model of statistical mechanics of Boltzmann is described and employed to derive the invariant modified forms of the first and the second laws of thermodynamics. The nature of De Pretto number 8338 that occurs in his mass-energy equivalence equation (De Pretto, 1903)

E = mc² = mc²/8338

and its identification as the universal gas constant are discussed. The invariant model of statistical mechanics is also shown to reveal the universal nature of the laws of thermodynamics in accordance with the perceptions of Boltzmann (Renn, 2000)

By application of the statistical method to arbitrary bodies (their treatment, so to say, as gas molecules with very many atoms) one can find mechanical systems which show full mechanical analogy with warm bodies,33 not only a partial one as the cyclic systems of Helmholtz. (Boltzmann and Babl 1905, p.549)

Invariant forms of Boltzmann distribution function, Planck energy spectrum as well as Maxwell-Boltzmann speed distribution for equilibrium statistical fields including that of isotropic stationary turbulence are presented. The results lead to the definitions of (electron, photon, neutrino) respectively as the most-probable equilibrium sizes of (photon, neutrino, tachyon) clusters. A scale-invariant model of statistical mechanics is also applied to derive the invariant forms of the conservation equations for mass, energy, and linear and angular momentum. The physical basis for the coincidence of normalized spacings between zeros of Riemann zeta function and the normalized Maxwell-Boltzmann distribution and its connections to Riemann Hypothesis are examined.

Brief Biography of the Speaker:
Siavash H. Sohrab received his PhD in Engineering Physics in 1981 from University of California, San Diego, his MS degree in Mechanical Engineering from San Jose State University in 1975, and his BS degree in Mechanical Engineering from the University of California, Davis in 1973. He joined Northwestern University in 1982 and since 1990 he is Associate Professor of Mechanical Engineering at the Northwestern University.