In order to understand observable signatures from putative cosmic-ray (CR) sources in-source acceleration of particles, their energy and time-dependent transport including interactions in an evolving environment and their escape from source have to be considered, in addition to source-to-Earth propagation.

We present the code CR-ENTREES (Cosmic-Ray ENergy TRansport in timE-Evolving astrophysical Settings) that evolves the coupled time- and energy-dependent kinetic equations for cosmic-ray nucleons, pions, muons, electrons, positrons, photons and neutrinos in a one-zone setup of (possibly) non-constant size, with user-defined particle and photon injection laws. All relevant interactions, particle/photon escape and adiabatic losses are considered in a radiation-dominated, magnetized astrophysical environment that is itself evolving in time. Particle and photon interactions are pre-calculated using event generators assuring an accurate interactions and secondary particle production description. We use the matrix multiplication method for fast radiation and particle energy transport which allows also an efficient treatment of transport non-linearities due to the produced particles/photons being fed back into the simulation chain.

Examples for the temporal evolution of the non-thermal emission from AGN jet-like systems with focus on proton-initiated pair cascades inside an expanding versus straight jet emission region, are further presented.