Gibbs states defined by biorthogonal sequences
  Motivated by the growing interest on PT-quantum mechanics, in this paper we discuss some facts on generalized Gibbs states and on their related KMS-like conditions. To achieve this, we first consider some useful connections between similar (Hamiltonian) operators and we propose some extended version of the Heisenberg algebraic dynamics, deducing some of their properties, useful for our purposes. 
Fabio Bagarello, Camillo Trapani, Salvatore Triolo
math-ph math.MP quant-ph