Molecular dynamics (MD) simulation has been widely used to study phonon-mediated thermal transport problems. The most common way of extracting the spectral phonon properties from MD simulations is through statistics-based methods, such as the normal mode analysis and spectral energy density analysis. However, these methods cannot effectively recognize the instantaneous changes in the decay of a phonon state after individual scattering events, meaning that they are unsuitable for use with systems undergoing transient processes at non-equilibrium. Previously, we have introduced a different approach called the perturbation-tracking (PT) method, and demonstrated its efficiency and accuracy in acquiring phonon properties. In this work, the PT method is employed to probe phonon scattering rates (inverse of relaxation times) in a non-equilibrium system modeled by EDIP crystalline silicon. Here we focus on anharmonic phonon-phonon scattering only so do not blend in other scattering sources. Since quantum effects are not included in classical MD simulations, the Bose-Einstein (B-E) distribution can be thought of and used as a non-equilibrium distribution. The non-equilibrium system is created with its initial phonon energy distribution complying with the B-E distribution and allowed to evolve freely after MD timesteps start; it finally reaches thermodynamic equilibrium after sufficient relaxation. We find that a non-equilibrium distribution with relatively small deviations from equilibrium can have considerable impacts on phonon-phonon interactions and markedly alter the scattering rates. And changes to the spectral energy distribution of portion frequencies affect scattering rates extensively over the whole spectrum of phonon modes. Since the PT method does not require statistical averaging for data processing, it can be used to track the variations in a phonon state and extract scattering rates in real time; this makes it a powerful tool for studying transient processes.