Dimensionless Fluctuation Balance Principle: New Statistical Perspectives Applied to Boltzmann, Planck, Fermi-Dirac, Bose-Einstein and Schr\"odinger Distributions

TL;DR

This paper introduces the Dimensionless Fluctuation Balance Principle, a novel approach to deriving fundamental statistical distributions in physics through fluctuation analysis, unifying various distributions under a common framework.

Contribution

It presents a new principle that derives key physics distributions from fluctuation balance, offering a unified and general foundation for statistical physics and related fields.

Findings

Successfully derived Boltzmann, Planck, Fermi-Dirac, Bose-Einstein, and Schrödinger distributions.

Provides a general framework for exchanging physical quantities in distribution models.

Applicable to diverse areas like quantum mechanics, nanomaterials, and material modeling.

Abstract

In this work we propose a completely new way to obtain statistics distributions from fluctuations balance. By dimensionless fluctuation analysis we obtain Boltzmann, Planck, Fermi-Dirac, Bose-Einstein and Schr\"odinger Distributions using the same fundamental principle. Our result point to a general foundation that was successful verified to principal Physics Distributions. We name it as Dimensionless Fluctuation Balance Principle. This is a great achievement which enable us to discuss exchange between different physical quantities, like we do when treat energy conservation when some type of energy is converted to another, but with more generality, because we can exchange one physical quantity to any other. All physics model which needs distribution can take advantage of methodology presented in this paper including: Statistical Physics, Schr\"odinger's Quantum Mechanics, Nanomaterials, Thin Films and New Materials Modeling. Keywords: Fluctuations, PDEs, Boltzmann, Planck, Entropy, Fermi-Dirac, Bose-Einstein, Schr\"odinger, Distributions.