2025/05/19 by Chung, Won Sang, Nieto, L. M., Zare, Soroush +1
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2505.15846
In this work, we explore both the ordinary q-Gaussian distribution and a new one defined here, determining both their mean and variance, and we use them to construct solutions of the q-deformed diffusion differential equation. This approach allows us to realize that the standard deviation of the distribution must be a function of time. In one case, we derive a linear Fokker-Planck equation within a finite region, revealing a new form of both the position- and time-dependent diffusion coefficient and the corresponding continuity equation. It is noteworthy that, in both cases, the conventional result is obtained when q tends to zero. Furthermore, we derive the deformed diffusion-decay equation in a finite region, also determining the position- and time-dependent decay coefficient. A discrete version of this diffusion-decay equation is addressed, in which the discrete times have a uniform interval, while for the discrete positions the interval is not uniform.