Tsallis, Rényi, and Shannon entropies for time-dependent mesoscopic RLC circuits

Abstract

We calculate information measures using the Tsallis, Rényi, and Shannon entropies for two classes (Lane–Emden and Caldirola–Kanai) of time-dependent mesoscopic RLC circuits. To determine the expressions for the entropies, we used the dynamical invariant method to obtain the exact Schrödinger wave function $\big (\psi _n (x,t)\big)$. For the state $n=0$, all the expressions found are given in terms of $\rho $, a c-number quantity satisfying a nonlinear differential equation. For the Caldirola–Kanai system, the entropies do not vary with time, but decrease with increasing damping factor. For the Lane–Emden system, the entropies decrease with increasing time. We also analyze the behavior of the Shannon and Rényi lengths in the charge and magnetic flux spaces and compare them with the respective standard deviations.