Fractal and entropy studies of Cherenkov arrival times

In this paper, time structure of simulated Cherenkov arrival times is explored by studying its multifractal/fractal and entropy properties. It is observed that the simulated Cherenkov arrival times are multifractal in nature. Its multifractal features do not show any dependence on the nature of the initiating particle and on the energy of arriving Cherenkov photons. However, the computed values of the entropy and Hausdorff dimension show consistent energy dependence on the energy of incoming γ-ray showers both for time arrivals as well for number of photons. Our results get partially validated by applying them to light curve of a gamma ray burst.