White Paper on Symmetric q-Decay and Its Applications

Abstract: This white paper examines the extension of classical radioactive decay theory using quan- tum calculus (q-calculus), a mathematical basis that generalizes traditional calculus by introducing a deformation parameter, q. It provides an in-depth theoretical background, including the development of q-exponential decay laws for q < 1, q > 1, and q = 1. A sample calculation showcases the applica- tion of q-calculus in decay modeling. The paper also explores the relevance of this model in various scientific fields, including nuclear physics, astrophysics, material science, and cosmology, with a par- ticular focus on modeling the hypothetical decay of dark matter particles, climate change dynamics, and cosmochemistry. The paper is complemented by relatively rigorous mathematical formulations and thought-provoking problems.