Abstract
Quantum thermodynamics is a research field that aims at fleshing out the ultimate limits of thermodynamic processes in the deep quantum regime. A complete picture of thermodynamical processes naturally allows for auxiliary systems dubbed ‘catalysts’, i.e., any physical systems facilitating state transformations while remaining essentially intact in their state, like an auxiliary system, a clock, or an actual catalyst. In this work, we present a comprehensive analysis of the power and limitation of such thermal catalysis. Specifically, we provide a family of optimal catalysts that can be returned with minimal trace distance error after facilitating a state transformation process. To incorporate the genuine physical role of a catalyst, we identify very significant restrictions on arbitrary state transformations under dimension or mean energy bounds, using methods of convex relaxations. We discuss the implication of these findings on possible thermodynamic state transformations in the quantum regime.
Highlights
In chemical reactions, it is common that a certain reaction should in principle be allowed, but in reality cannot take place because of the presence of some large energy barrier
The power of thermal embezzling We begin by exploring the case for trivial Hamiltonians, where it is known that thermal embezzling can occur
The sole conditions governing a transition from some quantum state ρ to σ is that the eigenvalue vector of ρ majorizes that of σ [2]
Summary
It is common that a certain reaction should in principle be allowed, but in reality cannot take place (or occurs at extremely low rates) because of the presence of some large energy barrier. The notion of TO means allowing for the full set of global unitaries which are energy preserving in the presence of some thermal bath This is a healthy and fruitful standpoint, and allows the application of many concepts and powerful tools derived from information theory [14,15,16]. This class entails all those thermodynamic processes that one can realistically physically implement in the presence of thermal baths, when encompassing real-world situations [17]. This seems a most natural view in light of the emerging limitations
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