We discuss generalized exponentials, whose inverse functions are at the core of generalized entropy formulas, with respect to particle-hole (KMS) symmetry.

The latter is fundamental in field theory; so, possible statistical generalizations of the Boltzmann formula-based thermal field theory have to take this property into account.

We demonstrate that Kaniadakis’ approach is KMS ready and discuss possible further generalizations.

T.S. Biró, Kaniadakis Entropy Leads to Particle–Hole Symmetric Distribution, Entropy (Basel) 24(9) (2022) e24091217