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 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 apply our technique to generic N identical interacting d-level quantum systems. Using permutation invariance, we find that, for large N, entropy displays a universal large deviation behavior with a rate 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 partition function is shown to satisfy a large deviation principle with a free energy f(x)=e(x)-β^-1s(x), where e(x) is a rate function that only depends on the ground state energy of particular subspaces determined by group representation theory. 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.