Phonons and magnons are low energy quasiparticles that determine many of key properties of nano-structured materials, such as heat transport in CPUs or operation of spintronic devices among others. Latest generation of monochromators introduced to scanning transmission electron microscopy in 2014 has granted microscopists an access to new domains of physics of excitation processes. Vibrational spectroscopy is a rapidly developing field, today reaching atomic scale spatial resolutions. At the level of theory, excitations of phonons were previously considered as "quasi-elastic" processes, since they could not be distinguished separately from the elastic scattering. Existing alternative descriptions based on quantum mechanical transition matrix elements are computationally expensive and hard to apply to systems with defects, interfaces, surfaces. We will employ non-equilibrium molecular dynamics simulations with so called colored thermostats, which allow to selectively heat (excite) a narrow range of energies of phonons. In subsequent steps one can use existing efficient approaches circumventing explicit calculations of transition matrix elements, offering thus a versatile and extremely efficient path to simulation of vibrational spectra in transmission electron microscopes with full access to arbitrary beam, detector and sample geometries. Analogous methods will be employed to magnetic scattering processes: dynamics of the precession of magnetic moments will be treated by non-equilibrium atomistic spin dynamics calculations with colored thermostats. Classical multislice method will be replaced by Pauli multislice method, which fully takes into account microscopic magnetic fields. These are the key components for building foundations of a theory and an efficient way of simulations of magnon scattering in transmission electron microscopy. Last but not least, theories developed in this project will permit simulations of time and temperature dependent processes.