From Harmonic Oscillators to Multiplicity Distributions in Particle Production Processes

We propose an oscillator framework of studying multi-particle production processes using the information theory approach. For a system of degenerate oscillators, we derive the negative binomial distribution (NBD) and its nonadditive generalization represented as gNBD. We observe that gNBD derived from nonadditive statistics describes data in higher multiplicity region, thereby providing an alternative for the multi-component distributions used in phenomenological studies. We also generalize our framework for non-degenerate oscillators and encounter a Lerch-type generalization of the Barnes zeta function that, to the best of our knowledge, has not been studied in the context of nonadditive statistics and multiplicity studies before.