A constraint on local definitions of quantum internal energy

Abstract

Recent advances in quantum thermodynamics have been focusing on ever more elementary systems of interest, approaching the limit of a single qubit, with correlations, strong coupling and non-equilibrium environments coming into play. Under such scenarios, it is clear that fundamental physical quantities must be revisited. This article questions whether a universal definition of internal energy for open quantum systems may be devised, setting limits on its possible properties. We argue that, for such a definition to be regarded as local, it should be implemented as a functional of the open system's reduced density operator and its time derivatives. Then we show that it should involve at least up to the second-order derivative, otherwise failing to recover the previously-known internal energy of the "universe". Possible implications of this general result are discussed.

20 pages, 3 figures. Version 2: new references added; further discussions on the hypotheses and connection to other approaches included in Sections I and V. Version 3: bibliographic metadata included

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Cited by in corpus (4)

• A Schmidt decomposition approach to quantum thermodynamics
• Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion
• Energy additivity as a requirement for universal quantum thermodynamical frameworks
• On the energetic analysis of autonomous quantum systems