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Quantum systems of indistinguishable particles are commonly described usingthe formalism of second quantisation, which relies on the assumption that anyadmissible quantum state must be either symmetric or anti-symmetric underparticle permutations. Coherence-induced many-body effects such assuperradiance, however, can arise even in systems whose constituents are notfundamentally indistinguishable as long as all relevant dynamical observablesare permutation-invariant. Such systems are not confined to symmetric oranti-symmetric states and therefore require a different theoretical approach.Focusing on non-interacting systems, here we combine tools from representationtheory and thermodynamically consistent master equations to develop such aframework. We characterise the structure and properties of the steady statesemerging in permutation-invariant ensembles of arbitrary multi-level systemsthat are collectively weakly coupled to a thermal environment. As anapplication of our general theory, we further explore how these states can inprinciple be used to enhance the performance of quantum thermal machines. Ourgroup-theoretical framework thereby makes it possible to analyse variouslimiting cases that would not be accessible otherwise. In addition, it allowsus to show that the properties of multi-level ensembles differ qualitativelyfrom those of spin ensembles, which have been investigated earlier using thestandard Clebsch-Gordan theory. Our results have a large scope for futuregeneralisations and pave the way for systematic investigations of collectiveeffects arising from permutation-invariance in quantum thermodynamics.

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