  We study non-Markovian effects present in a driven qubit coupled to a finite
environment using a recently proposed model developed in the context of
calorimetric measurements of open quantum systems. To quantify the degree of
non-Markovianity we use the Breuer-Laine-Piilo (BLP) measure [Breuer \textit{et
al.}, Phys. Rev. Lett. \textbf{103}, 210401 (2009)]. We show that information
backflow only occurs in the case of driving in which case we investigate the
dependence of memory effects on the environment size, driving amplitude and
coupling to the environment. We show that the degree of non-Markovianity
strongly depends on the ratio between the driving amplitude and the coupling
strength. We also show that the degree of non-Markovianity does not decrease
monotonically as a function of the environment size.
