  Understanding the behaviour of a quantum system coupled to its environment is
of fundamental interest in the general field of quantum technologies. It also
has important repercussions on foundational problems in physics, such as the
process of decoherence and the so-called quantum measurement problem. There
have been many approaches to explore Markovian and non-Markovian dynamics
within the framework of open quantum systems, but the richness of the ensuing
dynamics is still not fully understood. In this paper we develop a
non-Markovian extension of the standard Caldeira-Leggett model, based on
expanding the dynamics of the reduced system at high temperature in inverse
powers of the high-frequency cut-off of the Ohmic spectral density of the
environment, and derive a non-Markovian master equation for the reduced density
matrix for the case of a general potential. We also obtain a fully analytical
solution in the free particle case. While the short-time behaviour of this
solution does not diverge substantially from the Markovian behaviour, at
intermediate times we find a resurgence of coherence, which we name lateral
coherence. We identify this with a corresponding transient negative entropy
production rate, which is understood to be characteristic of non-Markovian
dynamics. We also analyze the positivity of the reduced density matrix, and
derive the corresponding Fokker-Planck equation in the classical limit.
