Abstract
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is 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. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.
Highlights
These limitations mean that while some states can still be created under the restricted class of operations, other state transformations can only be done with the help of additional resources
We show that a theory which satisfies the asymptotic equivalence property is reversible, that is, the amount of resources exchanged with the batteries during an asymptotic state transformation mapping ρ into σ is equal, with negative sign, to the amount of resources exchanged when mapping σ into ρ
If we allow the agent to use a thermal bath as a bank, and we keep the system decoupled from it, we find that changing a single resource, either energy or information, is enough to perform a generic state transformation on the system
Summary
Since the agent can use the bank to inter-convert between resources, they can decide to invest a higher amount of one resource to save on the others This freedom is reflected in our framework by a single relation, the first law of resource theories, which connects the different resources, each of them weighted by the corresponding exchange rate, to the change of a particular monotone between the initial and final state of the system, see Cor. 13. This equality is a generalisation of the first law of thermodynamics, where the sum of the work performed on the system and the heat absorbed from the environment is equal to the change in internal energy of the system.
Sign-in/Register to view highlights & summary 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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
