Una formulazione probabilistica del principio di esclusione di Pauli nel contesto delle inferenze predittive

Abstract

A unified derivation of Elementary Particle Statistics is hindered by Pauli's Exclusion Principle, that limits the possible states of the physical system in a peculiar way. It follows that if the Principle does not hold (Maxwell-Boltzmann e di Bose-Einstein cases) all occupation vectors are regular, so long as they are allowed by the macroscopic parameters. On the contrary, if the Principe holds (Fermi-Dirac case), the regularity domain of the probabilistic description is narrowed by the Principle itself. In this paper a recursive definition of regularity is proposed, able to unify the three Statistics. In this general formulation Pauli's Exclusion Principle can be found as a particular case. The paper is based on the notion of stochastic process with exchangeable increments. It can be considered as an unified approach to predictive inductive inferences from the particular point of view of Statistical Physics.