par Schonberg, Mario
Référence Il Nuovo cimento, 10, 4, page (1-54)
Publication Publié, 1953-04
Article révisé par les pairs
Résumé : The classical mechanics of indistinguishable particles discussed in I is further developed. The mechanical foundations of thermodynamics are discussed with the classical wave theory and the "quantized" fields in phase space. It is shown that the formalism eliminates automatically the Gibbs paradox. The classical statistics is treated with the Gibbs-von Neumann method and also by a generalized form of the Boltzmann method which allows to take into account the interactions. The introduction of finite cells in phase space leads to formulas similar to those of the quantal statistics for free particles, but no, more so for interacting particles. The statistical treatment of the «quantized» field in phase space leads immediately to the canonical grand ensemble. It is shown that the theory of the «quantized» fields in phase space can be derived from the theory of a «non-quantized» field in phase space, in which there are only continuous distributions of matter, by a procedure of «quantization» altogether similar to that of the quantum theory of fields, but not involving the Planck constant, or any other universal constant. The «non-quantized» field in phase space corresponds to a theory less accurate than the classical mechanics and gives an approximation of the same kind as the molecular chaos hypothesis of the kinetic gas theory, it contains both the dynamics and the heat theory of a continuous medium. A new derivation of the Boltzmann equation involving a special kind of time average is given and a similar equation is established for the two particle distribution function. © 1953 Società Italiana di Fisica.