  We investigate the physical property of the kappa parameter and the
kappa-distribution in the kappa-deformed statistics, based on Kaniadakis
entropy, for a relativistic gas in an electromagnetic field. We derive two
relations for the relativistic gas in the framework of kappa-deformed
statistics, which describe the physical situation represented by the
relativistic kappa-distribution function, provide a reasonable connection
between the parameter kappa, the temperature four-gradient and the four-vector
potential gradient, and thus present for the case kappa different from zero a
clearly physical meaning. It is shown that such a physical situation is a
meta-equilibrium state of the system, but has a new physical characteristic.
