When thermodynamical quantities are associated with quantum systems a question arises how to treat scenarios where the notion of temperature could exhibit some quantum features. It is known that the temperature of a gas in thermal equilibrium is not constant in a gravitational field, but it is not known how a delocalised quantum system would thermalise with such a bath. In this theoretical work we demonstrate two scenarios in which the notion of a 'superposition of temperatures' arises. First: a probe interacting with different baths dependent on the state of another quantum system (control). Second: the probe interacting with a bath in a superposition of purified states, each associated with a different temperature. We show that these two scenarios are fundamentally different and can be operationally distinguished. Moreover, we show that the probe does not in general thermalise even when the involved temperatures of the baths or purifications are equal. Furthermore, we show the final probe state depends on the specific realisation of the thermalising channels, being sensitive to the particular Kraus representations of the channels. This point appears to explain recent results obtained in the context of quantum interference of relativistic particle detectors thermalising with Unruh or Hawking radiation. Finally, we show that these results are reproduced in partial and pre-thermalisation processes, and thus our approach and conclusions also generally apply beyond the idealised scenarios, where thermalisation is not exact.

No abstract

No abstract

No abstract