  The standard (non-relativistic) $\kappa$-distribution is widely used to fit
data and to describe macroscopic thermodynamical behavior, e.g.\ the pressure
(temperature) as the second moment of the distribution function. By contrast to
a Maxwellian distribution, for small relevant values $\kappa < 2$ there exists
a significant, but unphysical contribution to the pressure from unrealistic,
superluminal particles with speeds exceeding the speed of light. Similar
concerns exist for the entropy. We demonstrate here that by using the recently
introduced regularized $\kappa$-distribution one can avoid such unphysical
behaviour.
