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We show how using a special relativistic kinetic equation with a BGK- likecollision operator the ensuing expression for the heat flux can be casted inthe form required by Classical Irreversible Thermodynamics. Indeed, it islinearly related to the temperature and number density gradients and not to theacceleration as the so-called "first order in the gradients theories" contend.Here we calculate explicitly the ensuing transport coefficients and comparethem with the results obtained by other authors.

The heat flux from a relativistic kinetic equation with a simplified collision kernel