Characterizing symmetry-protected thermal equilibrium by work extraction

• URL: http://arxiv.org/abs/2103.06060v2
• Date: Thu, 11 Mar 2021 09:59:38 GMT
• Title: Characterizing symmetry-protected thermal equilibrium by work extraction
• Authors: Yosuke Mitsuhashi, Kazuya Kaneko, Takahiro Sagawa
• Abstract summary: A quantum state is completely passive if work cannot be extracted from any number of copies of the state by any unitary operations. We prove that a quantum state is completely passive under a symmetry constraint described by a connected compact Lie group. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Symmetry induced enhancement in finite-time thermodynamic trade-off relations [0.0]
  We show a symmetry-based framework that describes the fundamental limit of collective enhancement in finite-time thermodynamics. We explicitly construct an open quantum system model that goes beyond the enhancement realized by the conventional superradiance model.
  arXiv  Detail & Related papers  (2024-08-08T07:39:00Z)
• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models [0.0]
  A class of nonintegrable bond-staggered models is endowed with a large number of zero-energy eigenstates and possesses a non-Abelian internal symmetry. We show that few-magnon zero-energy states have an exact analytical description, allowing us to build a basis of low-entangled fixed-separation states.
  arXiv  Detail & Related papers  (2024-07-16T17:48:47Z)
• Theory of Eigenstate Thermalisation [0.0]
  The eigenstate thermalization hypothesis (ETH) of Deutsch and Srednicki suggests that this is possible because each eigenstate of the full quantum system acts as a thermal bath to its subsystems. Our analysis provides a derivation of statistical mechanics which requires neither the concepts of ergodicity or typicality, nor that of entropy.
  arXiv  Detail & Related papers  (2024-06-03T15:41:16Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Asymmetry activation and its relation to coherence under permutation operation [53.64687146666141]
  A Dicke state and its decohered state are invariant for permutation. When another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation.
  arXiv  Detail & Related papers  (2023-11-17T03:33:40Z)
• Non-Abelian symmetry can increase entanglement entropy [62.997667081978825]
  We quantify the effects of charges' noncommutation on Page curves. We show analytically and numerically that the noncommuting-charge case has more entanglement.
  arXiv  Detail & Related papers  (2022-09-28T18:00:00Z)
• Thermodynamics of Permutation-Invariant Quantum Many-Body Systems: A Group-Theoretical Framework [0.0]
  Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation. Coherence-induced many-body effects such as superradiance can arise even in systems whose constituents are not fundamentally indistinguishable.
  arXiv  Detail & Related papers  (2022-06-25T12:48:49Z)
• Quantum Mechanics as a Theory of Incompatible Symmetries [77.34726150561087]
  We show how classical probability theory can be extended to include any system with incompatible variables. We show that any probabilistic system (classical or quantal) that possesses incompatible variables will show not only uncertainty, but also interference in its probability patterns.
  arXiv  Detail & Related papers  (2022-05-31T16:04:59Z)
• Gauge Quantum Thermodynamics of Time-local non-Markovian Evolutions [77.34726150561087]
  We deal with a generic time-local non-Markovian master equation. We define current and power to be process-dependent as in classical thermodynamics. Applying the theory to quantum thermal engines, we show that gauge transformations can change the machine efficiency.
  arXiv  Detail & Related papers  (2022-04-06T17:59:15Z)
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain [0.0]
  We show that relaxation of driven-dissipative systems after a quantum quench can be determined by a maximum entropy ensemble. We show that these results apply to broad classes of noninteracting fermionic models.
  arXiv  Detail & Related papers  (2022-03-28T08:59:58Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.