  In this thesis, I investigate various aspects of one of the most fundamental
questions in thermodynamics: what state transformations can quantum systems
undergo while interacting with a thermal bath under specific constraints? These
constraints may involve total energy conservation, memory effects, or
finite-size considerations. Addressing this question leads to (i) a
characterisation of the structure of the thermodynamic arrow of time, (ii) a
framework bridging the gap between memoryless and arbitrarily non-Markovian
thermodynamic processes, and (iii) a derivation of the famous
fluctuation-dissipation relation within a quantum information framework.
Finally, the last part of this thesis focuses on studying a ubiquitous
phenomenon in science, so-called catalysis. It involves using an auxiliary
system (a catalyst) to enable processes that would otherwise be impossible.
Over the last two decades, this notion has spread to the field of quantum
physics. However, this effect is typically described within a highly abstract
framework. Despite its successes, this approach struggles to fully capture the
behaviour of physically realisable systems, thereby limiting the applicability
of quantum catalysis in practical scenarios. Strikingly, I will demonstrate
this effect in a paradigmatic quantum optics setup, namely the Jaynes-Cummings
model, where an atom interacts with an optical cavity. The atom plays the role
of the catalyst and allows for the deterministic generation of non-classical
light in the cavity, as evidenced by sub-Poissonian statistics or Wigner
negativity.
