In the present effort, we revisit the Shannon entropy approach for the study of both the extent and the rate of diffusion in a given dynamical system. In particular, we provide a theoretical and numerical study of the dependence of the formulation on the parameters of the method. We succeed in deriving not only a diffusion coefficient, \(D_{S}\), but also an estimate of the macroscopical instability time for the system under study. Dealing with a toy model, namely a 4D symplectic application that represents the dynamics around a junction of resonances of different order, and an a particular case of the planar three-body problem, the HD20003 planetary system, we obtain numerical evidence that \(D_{S}\) is a robust measure of the diffusion rate, no significant dependence on the free parameter of the entropy formulation (the size of the elements of the partition) being observed. Moreover, successful results concerning the estimation of macroscopical instability times obtained from \(D_{S}\) are presented in both cases.

在当前的工作中，我们将重新研究香农熵方法，以研究给定动力学系统中扩散的程度和速度。特别是，我们提供了关于配方对方法参数的依赖性的理论和数值研究。我们不仅成功导出了扩散系数\（D_ {S} \），而且还得出了所研究系统的宏观不稳定时间的估计值。处理一个玩具模型，即一个4D辛应用，它表示围绕不同阶次共振的交界处的动力学，以及平面三体问题的特殊情况，即HD20003行星系统，我们得到了数值证据，证明\（D_ {S} \）是对扩散速率的可靠度量，对所观察到的熵公式的自由参数（分隔元素的大小）没有显着依赖。此外，在两种情况下都给出了关于从\（D_ {S} \）获得的宏观不稳定性时间的估计的成功结果。