A hierarchy of thermal processes collapses under catalysis

Thermal operations (TO) are a generic description for allowed state transitions under thermodynamic restrictions. However, the quest for simpler methods to encompass all these processes remains unfulfilled. We resolve this challenge through the catalytic use of thermal baths, which are assumed to be easily accessible. We select two sets of simplified operations: elementary TO (ETO) and Markovian TO (MTO). They are known for their experimental feasibility, but fail to capture the full extent of TO due to their innate Markovianity. We nevertheless demonstrate that this limitation can be overcome when the operations are enhanced by ambient-temperature Gibbs state catalysts. In essence, our result indicates that free states within TO can act as catalysts that provide the necessary non-Markovianity for simpler operations. Furthermore, we prove that when any catalyst can be employed, different thermal processes (TO, ETO, and MTO) converge. Notably, our results extend to scenarios involving initial states with coherence in the energy eigenbasis, a notoriously difficult process to characterise.