## Abstract

A scale invariant model of statistical mechanics is applied to derive invariant Maxwell-Boltzmann speed and Planck energy spectrum of equilibrium statistical fields including that of isotropic stationary turbulence. The latter is shown to lead to the definitions of (electron, photon, neutrino) respectively as the most-probable equilibrium sizes of (photon, neutrino, tachyon) clusters. Also, invariant modified form of the first law of thermodynamics is derived and a modified definition of entropy, invariant forms of transport coefficients, and hierarchies of absolute zero temperatures and vacua are described. 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. New paradigms for hydrodynamic foundations of both Schrödinger as well as Dirac wave equations are discussed.

Original language | English (US) |
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Title of host publication | Proceedings of the European Computing Conference, ECC '11 |

Pages | 427-455 |

Number of pages | 29 |

State | Published - Sep 29 2011 |

Event | European Computing Conference, ECC '11 - Paris, France Duration: Apr 28 2011 → Apr 30 2011 |

### Other

Other | European Computing Conference, ECC '11 |
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Country | France |

City | Paris |

Period | 4/28/11 → 4/30/11 |

## Keywords

- Kinetic theory of ideal gas
- Riemann hypothesis
- Statistical mechanics
- TOE
- Thermodynamics

## ASJC Scopus subject areas

- Computational Theory and Mathematics
- Theoretical Computer Science