  We study the dynamics of a spin-1/2 particle interacting with a multi-spin
environment, modelling the corresponding open system dynamics through a
collision-based model. The environmental particles are prepared in individual
thermal states, and we investigate the effects of a distribution of
temperatures across the spin environment on the evolution of the system,
particularly how thermalisation in the long-time limit is affected. %We also
address the conditions under which the system reaches a stationary state, with
particular attention to whether homogenization to the average environmental
state occurs. We study the phenomenology of the heat exchange between system
and environment and consider the information-to-energy conversion process,
induced by the system-environment interaction and embodied by the Landauer
principle. Furthermore, by considering an interacting-particles environment, we
tune the dynamics of the system from an explicit Markovian evolution up to a
strongly non-Markovian one, investigating the connections between
non-Markovianity, the establishment of system-environment correlations, and the
breakdown of the validity of Landauer principle.
