Uploaded July 2018 | Updated September 2026, 6 hours ago
We derive conditions for the interconversion of resources, that is, for the existence of a `first law of thermodynamics’ within arbitrary quantum resource theories. Resource theories are versatile tools that characterise several aspects of quantum physics, from entanglement to thermodynamics. Usually one identifies a single quantity as the resource associated with the theory: in studying non-locality the resource is entanglement, while for thermodynamics it can be work. In reality, we often need more than a single resource in order to perform a given task: for instance, the power of quantum computation relies on both purity (of the input qubits), and coherence (created by the gates).
Here we introduce a general framework to describe tasks requiring multiple resources in quantum settings. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory plays a fundamental role in the quantification of the resources. Finally, we analyse the interconversion of resources, introducing a first law for general multi-resource theories – a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. We apply these results to thermodynamics with multiple conserved charges, and to the theory of local control under energetic restrictions.
Annual UWO Philosophy of Physics Conference
Thermodynamics as a Resource Theory: Foundational and Philosophical Implications
June 20-22, 2018
philphysics.uwo.ca
Carlo Sparaciari, University College, London
Visit the Rotman website for more information on applications, events, project descriptions, and openings. rotman.uwo.ca
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We derive conditions for the interconversion of resources, that is, for the existence of a `first law of thermodynamics’ within arbitrary quantum resource theories. Resource theories are versatile tools that characterise several aspects of quantum physics, from entanglement to thermodynamics. Usually one identifies a single quantity as the resource associated with the theory: in studying non-locality the resource is entanglement, while for thermodynamics it can be work. In reality, we often need more than a single resource in order to perform a given task: for instance, the power of quantum computation relies on both purity (of the input qubits), and coherence (created by the gates).
Here we introduce a general framework to describe tasks requiring multiple resources in quantum settings. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory plays a fundamental role in the quantification of the resources. Finally, we analyse the interconversion of resources, introducing a first law for general multi-resource theories – a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. We apply these results to thermodynamics with multiple conserved charges, and to the theory of local control under energetic restrictions.
Annual UWO Philosophy of Physics Conference
Thermodynamics as a Resource Theory: Foundational and Philosophical Implications
June 20-22, 2018
philphysics.uwo.ca
Carlo Sparaciari, University College, London
Visit the Rotman website for more information on applications, events, project descriptions, and openings. rotman.uwo.ca
Follow The Rotman Institute on Twitter: twitter.com/rotmanphilo
Like The Rotman Institute on Facebook: facebook.com/rotmanphilosophy
Subscribe to our channel: youtube.com/user/rotmanphilosophy
