Non-Hermitian quantum networks and configuration entropy: Negative temperatures

Using the ordered product for quantum operators, the motion equation in a quantum network with discrete charge is solved exactly. More importantly, by introducing dissipation, the non-Hermitian dynamics is treated, finding the exceptional point explicitly. It defines the energies supporting stationary states which are degenerate. Consequently, the configuration entropy is calculated. Entropy is a decreasing function of energy, a typical characteristic of dual metamaterials, which also sustains negative temperatures. The specific heat is also calculated as being always negative.