Determination of Shannon entropy and Fisher information of the Feshbach-Villars oscillator for spin-0 particles

This paper is devoted to calculating the Fisher and Shannon information parameters of the Feshbach-Villars oscillator (FVO) for spin-0 particles. Instead of the Klein-Gordon equation, the Feshbach-Villars formalism provides a positive probability density. By determining Fisher information and Shannon entropy, we assess the sensitivity of probability distributions to parameter changes and the degree of uncertainty. Our research provides insights into the dynamics and information-theoretic characteristics of spin-0 particles in both spatial and momentum configurations. This work advances our understanding of the quantum information properties of spin-0 particles and lays the groundwork for future developments in quantum computing and information theory. Finally, the Stam, Cramer–Rao, and Bialynicki–Birula–Mycielski (BBM) inequalities have been verified, and we demonstrated that the BBM inequality remains valid in the form \(S_{x}+S_{p}\ge 1+\ln \pi \) $S_x+S_p\ge 1+ln\pi$ , consistent with ordinary quantum mechanics.