Regensburg 2022 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 2: Quantum Thermodynamics and Open Quantum Systems

QI 2.3: Vortrag

Montag, 5. September 2022, 10:15–10:30, H9

Geometric structure of thermal cones — •Alexssandre de Oliveira Junior, Jakub Czarkowski, Karol Zyczkowski, and Kamil Korzekwa — Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland.

The second law of thermodynamics imposes a fundamental asymmetry in the flow of events. The so-called thermodynamic arrow of time introduces an ordering on the space of states that can be distinguished according to the system’s evolution as past, incomparable, and future thermal cones. In this work, we analyse the structure of the thermodynamic arrow of time within a resource-theoretic framework, where one investigates the accessibility of quantum state transformations under thermodynamic constraints. Specifically, for a d-dimensional classical state interacting with a heat bath at a fixed temperature T, we found the necessary and sufficient conditions to construct its incomparable and past thermal cones. By introducing a new thermodynamic monotone, the volume of the future thermal cone, we provide a detailed analysis of the behaviour of the thermal cones. In a general context, while the future thermal cone can be seen as a generalisation of the Hardy-Littlewood-Polya theorem, the past and incomparable region can be interpreted as its extensions. Moreover, our results also apply to other majorisation-based resource theories, such as entanglement, since in the limit of infinite temperature, the partial order that emerges is the same (precisely: the opposite) as defined on the set of bipartite pure entangled states by local operations and classical communication