Anomalous thermodynamics of lattice Bose gases in optical cavities

We investigate thermodynamic properties of lattice Bose gases in optical cavities in the Mott-insulator limit. We find the system assumes anomalous thermodynamic behavior that can be traced back to the breaking of fundamental additivity by its infinite-long range interaction. Specifically, the system shows striking ensemble inequivalence between the canonical ensemble and the grand canonical one, sharply manifesting in the distinct anomalous structure of the thermodynamic phase diagram in the canonical ensemble. In particular, in the temperature regime around half of the on-site energy, the system manifests negative compressibility and anomalous reentrant phase transitions where the ordered charge density wave phase revives from the disordered homogenous phase upon increasing the temperature. Direct experimental observation of the anomalous behavior can be realized in the current experiments with well-controlled total particle number fluctuations.