Thermodynamics of Permutation-Invariant Quantum Many-Body Systems: A Group-Theoretical Framework

Abstract

Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle permutations. Coherence-induced many-body effects such as superradiance, however, can arise even in systems whose constituents are not fundamentally indistinguishable as long as all relevant dynamical observables are permutation-invariant. Such systems are not confined to symmetric or anti-symmetric states and therefore require a different theoretical approach. Focusing on non-interacting systems, here we combine tools from representation theory and thermodynamically consistent master equations to develop such a framework. We characterise the structure and properties of the steady states emerging in permutation-invariant ensembles of arbitrary multi-level systems that are collectively weakly coupled to a thermal environment. As an application of our general theory, we further explore how these states can in principle be used to enhance the performance of quantum thermal machines. Our group-theoretical framework thereby makes it possible to analyse various limiting cases that would not be accessible otherwise. In addition, it allows us to show that the properties of multi-level ensembles differ qualitatively from those of spin ensembles, which have been investigated earlier using the standard Clebsch-Gordan theory. Our results have a large scope for future generalisations and pave the way for systematic investigations of collective effects arising from permutation-invariance in quantum thermodynamics.

arXiv comment19 + 7 pages, 7 figures. Close to published version. Comments welcome

References in corpus (61)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Quantum Thermodynamics
• Quantum Thermodynamic Cycles and quantum heat engines
• The second laws of quantum thermodynamics
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Quantum enhanced measurements without entanglement
• Quantum Adiabatic Markovian Master Equations
• Universal Lindblad equation for open quantum systems
• Quantum Thermodynamic Cycles and Quantum Heat Engines (II)
• Cavity Mediated Collective Spin Exchange Interactions in a Strontium Superradiant Laser
• Quantum Supremacy of Many-Particle Thermal Machines
• The work value of information
• Optimal cycles for low-dissipation heat engines
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Thermodynamic Geometry of Microscopic Heat Engines
• Enhanced Quantum Interface with Collective Ion-Cavity Coupling
• Thermodynamic length in open quantum systems
• Thermodynamic uncertainty relation in slowly driven quantum heat engines
• Periodic Thermodynamics of Open Quantum Systems
• Collective operation of quantum heat machines via coherence recycling, and coherence induced reversibility
• Work fluctuations in slow processes: quantum signatures and optimal control
• Completely positive master equation for arbitrary driving and small level spacing
• Time Dependent Markovian Quantum Master Equation
• Cooperative many-body enhancement of quantum thermal machine power
• An Interaction-Driven Many-Particle Quantum Heat Engine: Universal Behavior
• Quantum coherence, many-body correlations, and non-thermal effects for autonomous thermal machines
• Bosons Outperform Fermions -- The Thermodynamic Advantage of Symmetry
• Quantum Statistical Enhancement of the Collective Performance of Multiple Bosonic Engines
• Collective effects and quantum coherence in dissipative charging of quantum batteries
• An efficient non-linear Feshbach engine
• Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
• Many-body quantum thermal machines
• Nonequilibrium many-body quantum engine driven by time-translation symmetry breaking
• A non-equilibrium quantum many-body Rydberg atom engine
• Quantum-Enhanced Heat Engine Based on Superabsorption
• Speed-ups to isothermality: Enhanced quantum thermal machines through control of the system-bath coupling
• A photonic quantum engine driven by superradiance
• Boosting engine performance with Bose-Einstein condensation
• A many-body heat engine at criticality
• Asymptotics of Plancherel-type random partitions
• Geometry of work fluctuations versus efficiency in microscopic thermal machines
• Collective effects on the performance and stability of quantum heat engines
• Collective heat capacity for quantum thermometry and quantum engine enhancements
• Thermodynamics from indistinguishability: mitigating and amplifying the effects of the bath
• Detecting Hidden Differences via Permutation Symmetries
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• Quantum Heat Engines with Singular Interactions
• Superradiant many-qubit absorption refrigerator
• Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond
• A Feshbach engine in the Thomas-Fermi regime
• Enhanced energy transfer to an optomechanical piston from indistinguishable photons
• Validity of Born-Markov master equations for single and two-qubit systems
• Measurement and Particle Statistics in the Szilard Engine
• Discriminating distinguishability
• Performance of the collective three-level quantum thermal engine
• Limit cycles in periodically driven open quantum systems
• On multiplicities of irreducibles in large tensor product of representations of simple Lie algebras
• Mixing indistinguishable systems leads to a quantum Gibbs paradox
• Superradiance of a subwavelength array of independent classical nonlinear emitters
• Gibbs mixing of partially distinguishable photons with a polarising beamsplitter membrane
• Geometric Bounds on the Power of Adiabatic Thermal Machines

Cited by in corpus (10)

• Exotic synchronization in continuous time crystals outside the symmetric subspace
• Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines
• Floquet analysis of a superradiant many-qutrit refrigerator
• Quantum thermochemical engines
• Quantum dynamics of a fully-blockaded Rydberg atom ensemble
• Symmetry shapes thermodynamics of macroscopic quantum systems
• Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory
• Symmetry induced enhancement in finite-time thermodynamic trade-off relations
• Permutationally invariant processes in open multiqudit systems
• Scaling of symmetry-restricted quantum circuits