Abstract
In this brief paper, we compare two frameworks for characterizing possible operations in quantum thermodynamics. One framework considers thermal operations—unitaries which conserve energy. The other framework considers all maps which preserve the Gibbs state at a given temperature. Thermal operations preserve the Gibbs state; hence a natural question which arises is whether the two frameworks are equivalent. Classically, this is true—Gibbs-preserving maps are no more powerful than thermal operations. Here, we show that this no longer holds in the quantum regime: a Gibbs-preserving map can generate coherent superpositions of energy levels while thermal operations cannot. This gap has an impact on clarifying a mathematical framework for quantum thermodynamics.
Highlights
What’s more, we can explore what happens in regimes which had previously been difficult to study, in particular, we can gain a better understanding of thermodynamics at the quantum level
If a transition between initial and final states block diagonal in their energy eigenbasis is possible by Gibbs-preserving maps, it is possible via thermal operations [11]
Thermal operations include bringing in arbitrary systems which are in the Gibbs state at temperature T
Summary
The other framework considers all maps which preserve the Gibbs state at a given temperature. Among the various mathematical frameworks proposed to model thermodynamical operations, two have proven useful, namely the resource theory of thermal operations and the Gibbs-preserving maps. If a transition between initial and final states block diagonal in their energy eigenbasis is possible by Gibbs-preserving maps, it is possible via thermal operations [11].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
