The property of κ-deformed statistics for a relativistic gas in an electromagnetic field: κ parameter and κ-distribution

We investigate the physical property of the κ parameter and the κ-distribution in the κ-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 κ-deformed statistics, which describe the physical situation represented by the relativistic κ-distribution function, provide a reasonable connection between the parameter κ, the temperature four-gradient and the four-vector potential gradient, and thus present for the case κ≠0 one 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.