Characterizing symmetry-protected thermal equilibrium by work extraction

Abstract

The second law of thermodynamics states that work cannot be extracted from thermal equilibrium, whose quantum formulation is known as complete passivity; A state is called completely passive if work cannot be extracted from any number of copies of the state by any unitary operations. It has been established that a quantum state is completely passive if and only if it is a Gibbs ensemble. In physically plausible setups, however, the class of possible operations is often restricted by fundamental constraints such as symmetries imposed on the system. In the present work, we investigate the concept of complete passivity under symmetry constraints. Specifically, we prove that a quantum state is completely passive under a symmetry constraint described by a connected compact Lie group, if and only if it is a generalized Gibbs ensemble (GGE) including conserved charges associated with the symmetry. Remarkably, our result applies to non-commutative symmetry such as $SU(2)$ symmetry, suggesting an unconventional extension of the notion of GGE. Furthermore, we consider the setup where a quantum work storage is explicitly included, and prove that the characterization of complete passivity remains unchanged. Our result extends the notion of thermal equilibrium to systems protected by symmetries, and would lead to flexible design principles of quantum heat engines and batteries. Moreover, our approach serves as a foundation of the resource theory of thermodynamics in the presence of symmetries.

48 pages, 7 figures

References in corpus (5)

• Reference frames, superselection rules, and quantum information
• The Luttinger model following a sudden interaction switch-on
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Clock-Driven Quantum Thermal Engines
• How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics

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• Randomized measurement protocols for lattice gauge theories
• Unitary Designs of Symmetric Local Random Circuits
• A hierarchy of thermal processes collapses under catalysis
• Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis
• Key Observable for Linear Thermalization
• Optimal Work Extraction from Finite-Time Closed Quantum Dynamics
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group