Symmetry Shapes Thermodynamics of Macroscopic Quantum Systems

We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We first show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of the details of its density matrix. We then apply our technique to generic N identical interacting d-level quantum systems. Using permutation invariance, we find that, for large N, the entropy displays a universal asymptotic behavior in terms of a function s(x) that is completely independent of the microscopic details of the model, but depends only on the size of the irreducible representations of the permutation group S_{N}. In turn, the equilibrium state of the system and macroscopic fluctuations around it are shown to satisfy a large deviation principle with a rate function f(x)=e(x)-β^{-1}s(x), where e(x) only depends on the ground state energy of particular subspaces determined by group representation theory, and β is the inverse temperature. We apply our theory to the transverse-field Curie-Weiss model, a minimal model of phase transition exhibiting an interplay of thermal and quantum fluctuations.