  In this paper we calculate the entropy production of a relativistic binary
mixture of inert dilute gases using kinetic theory. For this purpose we use the
covariant form of Boltzmann's equation which, when suitably transformed, yields
a formal expression for such quantity. Its physical meaning is extracted when
the distribution function is expanded in the gradients using the well-known
Chapman-Enskog method. Retaining the terms to first order, consistently with
Linear Irreversible Thermodynamics we show that indeed, the entropy production
can be expressed as a bilinear form of products between the fluxes and their
corresponding forces. The implications of this result are thoroughly discussed.
